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Professor Jie Du

Professor Jie Du

Professor
Science
School of Mathematics & Statistics

Jie Du is a Professor in the School of Mathematics and Statistics.

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RESEARCH INTERESTS

Prof Du is a member of the School's Algebra and Number Theory and Combinatorics research groups. His interests lie in the representation theories on algebraic and quantum groups, finite groups of Lie type, finite dimensional algebras, and related topics. His recent works focus mainly on quantum supergroups, i-quantum groups, q-Schur algebras of super type, and their associated Schur-Weyl duality. He is also interested in combinatorics arising from generalised symmetric groups, Kazhdan-Lusztig cells and representations of finite algebras.

Phone
9385 7087
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room RC-4113
  • Books | 2012
    Deng B; Du J; Fu Q, 2012, A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory, Original, Cambridge University Press, UK
    Books | 2008
    Deng B; Du J; Parshall B; Wang J, 2008, Finite Dimensional Algebras and Quantum Groups, Original, American Mathematical Society, USA
  • Book Chapters | 2010
    Du J; Fu Q, 2010, 'Quantum gln, q-Schur algebras and their infinite/infinitesimal counterparts', in Gyoja A; Nakajima H; Shinoda K; Shoji T; Tanisaki T (ed.), Representation Theory of Algebraic Groups and Quantum Groups, Birkhauser, New York, pp. 93 - 119
  • Journal articles | 2024
    Du J; Gu H; Li Z; Wan J, 2024, 'Some Multiplication Formulas in Queer q-Schur Superalgebras', Transformation Groups,
    Journal articles | 2022
    Du J; Fu Q; Lin Y, 2022, 'A REALIZATION OF THE ENVELOPING SUPERALGEBRA μℚ(glm', Nagoya Mathematical Journal, 247, pp. 516 - 551,
    Journal articles | 2022
    Du J; Lin Y; Zhou Z, 2022, 'Quantum queer supergroups via Ï…-differential operators', Journal of Algebra, 599, pp. 48 - 103,
    Journal articles | 2022
    Du J; Wan J, 2022, 'Standard multipartitions and a combinatorial affine Schur-Weyl duality', Journal of Pure and Applied Algebra, 226,
    Journal articles | 2022
    Du J; Wu Y, 2022, 'A new realisation of the i-quantum group UÈ·(n)', Journal of Pure and Applied Algebra, 226,
    Journal articles | 2022
    Du J; Wu Y, 2022, 'THE i-QUANTUM GROUP Uı (n)', Pacific Journal of Mathematics, 320, pp. 61 - 101,
    Journal articles | 2020
    Du J; Lin Y; Zhou Z, 2020, 'Polynomial super representations of U-q(res) (gl(m vertical bar n)) at roots of unity', JOURNAL OF ALGEBRAIC COMBINATORICS, 51, pp. 195 - 235,
    Journal articles | 2020
    Du J; Lin Y; Zhou Z, 2020, 'Polynomial super representations of Uqres(glm', Journal of Algebraic Combinatorics, 51, pp. 195 - 235,
    Journal articles | 2020
    Du J; Zhou Z, 2020, 'The regular representation of UÏ…(Glm', Proceedings of the American Mathematical Society, 148, pp. 111 - 124,
    Journal articles | 2020
    Du JIE; Gu H; Zhou Z, 2020, 'MULTIPLICATION FORMULAS and SEMISIMPLICITY for q-SCHUR SUPERALGEBRAS', Nagoya Mathematical Journal, 237, pp. 98 - 126,
    Journal articles | 2019
    Deng B; Du J; Yang G, 2019, 'Slim cyclotomic q-Schur algebras', Journal of Algebra, 535, pp. 365 - 406,
    Journal articles | 2019
    Du J; Fu Q, 2019, 'The Integral Quantum Loop Algebra of gln', International Mathematics Research Notices, 2019, pp. 6179 - 6215,
    Journal articles | 2018
    Du J; Haixia G, 2018, 'q-Schur superalgebras', SCIENTIA SINICA Mathematica, 48, pp. 1571 - 1571,
    Journal articles | 2018
    Du J; Parshall BJ; Scott LL, 2018, 'Local and global methods in representations of Hecke algebras', Science China Mathematics, 61, pp. 207 - 226,
    Journal articles | 2018
    Du J; Wan J, 2018, 'The queer q-Schur superalgebra', Journal of the Australian Mathematical Society, 105, pp. 316 - 346,
    Journal articles | 2018
    Du J; Zhao Z, 2018, 'Multiplication formulas and canonical bases for Quantum Affine Gln', Canadian Journal of Mathematics, 70, pp. 773 - 803,
    Journal articles | 2017
    Du J; Gu H; Wang J, 2017, 'Representations of q-Schur superalgebras in positive characteristics', Journal of Algebra, 481, pp. 393 - 419,
    Journal articles | 2017
    Du J; Jensen BT; Su X, 2017, 'Presenting Hecke endomorphism algebras by Hasse quivers with relations', Journal of Pure and Applied Algebra, 221, pp. 883 - 907,
    Journal articles | 2017
    Du J; Parshall BJ; Scott LL, 2017, 'Stratifying endomorphism algebras using exact categories', JOURNAL OF ALGEBRA, 475, pp. 229 - 250,
    Journal articles | 2017
    Du J; Parshall BJ; Scott LL, 2017, 'Stratifying endomorphism algebras using exact categories', Journal of Algebra, 475, pp. 229 - 250,
    Journal articles | 2016
    Du J; Fu Q, 2016, 'Small Representations for Affine q-Schur Algebras', Algebras and Representation Theory, 19, pp. 355 - 376,
    Journal articles | 2015
    Du J; Fu Q, 2015, 'Quantum affine gln via Hecke algebras', Advances in Mathematics, 282, pp. 23 - 46,
    Journal articles | 2015
    Du J; Gu H, 2015, 'Canonical bases for the quantum supergroups U(glm', Mathematische Zeitschrift, 281, pp. 631 - 660,
    Journal articles | 2015
    Du J; Parshall BJ; Scott LL, 2015, 'Extending hecke endomorphism algebras', Pacific Journal of Mathematics, 279, pp. 229 - 254,
    Journal articles | 2015
    Du J; Wan J, 2015, 'Presenting queer Schur Superalgebras', International Mathematics Research Notices, 2015, pp. 2210 - 2272,
    Journal articles | 2014
    Du J; Gu H; Wang J, 2014, 'Irreducible representations of q-Schur superalgebras at a root of unity', Journal of Pure and Applied Algebra, 218, pp. 2012 - 2059,
    Journal articles | 2014
    Du J; Gu H, 2014, 'A realisation of the quantum supergroup U(glm', Journal of Algebra, 404, pp. 60 - 99,
    Journal articles | 2013
    Deng B; Du J, 2013, 'Identification of simple representations for affine q-Schur algebras', Journal of Algebra, 373, pp. 249 - 275,
    Journal articles | 2012
    Du J; Fu Q; Wang J, 2012, 'Representations of little q-Schur algebras', Pacific Journal of Mathematics, 257, pp. 343 - 378
    Journal articles | 2011
    Du J; Rui H, 2011, 'Quantum Schur superalgebras and Kazhdan-Lusztig combinatorics', Journal of Pure and Applied Algebra, 215, pp. 2715 - 2737,
    Journal articles | 2010
    Deng B; Du J, 2010, 'Presenting degenerate Ringel-Hall algebras of cyclic quivers', Journal of Pure and Applied Algebra, 214, pp. 1787 - 1799,
    Journal articles | 2010
    Du J; Deng B, 2010, 'Tight monomials and the monomial basis property', Journal of Algebra, 324, pp. 3355 - 3377,
    Journal articles | 2010
    Du J; Fu Q, 2010, 'A modified BLM approach to quantum affine gln', Mathematische Zeitschrift, 266, pp. 747 - 781,
    Journal articles | 2009
    Du J; Fu Q, 2009, 'Quantum g iota(infinity) infinite q-Schur algebras and their representations', Journal of Algebra, 322, pp. 1516 - 1547
    Journal articles | 2009
    Du J; Fu Q, 2009, 'Quantum gl∞, infinite q-Schur algebras and their representations', Journal of Algebra, 322, pp. 1516 - 1547,
    Journal articles | 2009
    Du J; Shu B, 2009, 'Representations of finite Lie algebras', Journal of Algebra, 321, pp. 3197 - 3225,
    Journal articles | 2007
    Deng B; Du J; Xiao J, 2007, 'Generic extensions and canonical bases for cyslic quivers', Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 59, pp. 1260 - 1283
    Journal articles | 2007
    Deng B; Du J; Zhang G, 2007, 'Linear quivers, generic extensions and Kashiwara operators', Indagationes Mathematicae - New Series, 18, pp. 3 - 21
    Journal articles | 2007
    Deng B; Du J, 2007, 'Folding derived categories with Frobenius functors', Journal of Pure and Applied Algebra, 208, pp. 1023 - 1050
    Journal articles | 2006
    Deng B; Du J, 2006, 'Algebras, representations and their derived categories over finite fields', Contemporary Mathematics, 413, pp. 25 - 41,
    Journal articles | 2006
    Deng B; Du J, 2006, 'Frobenius morphisms and representations of algebras', Transactions of the American Mathematical Society, 358, pp. 3591 - 3622
    Journal articles | 2005
    Deng B; Du J, 2005, 'Bases of quantized enveloping algebras', Pacific Journal of Mathematics, 220, pp. 33 - 48
    Journal articles | 2005
    Deng B; Du J, 2005, 'Monomial bases for quantum affine', Advances in Mathematics, 191, pp. 276 - 304,
    Journal articles | 2005
    Du J; Fu Q; Wang J, 2005, 'Infinitesimal quantum and little q-Schur algebras', Journal of Algebra, 287, pp. 199 - 233,
    Journal articles | 2005
    Du J, 2005, 'Robinson-Schensted algorithm and Vogan equivalence', Journal of Combinatorial Theory Series A, 112, pp. 165 - 172,
    Journal articles | 2004
    Du J; Lin Z, 2004, 'Stratifying algebras with near-matrix algebras', Journal of Pure and Applied Algebra, 188, pp. 59 - 72
    Journal articles | 2003
    Du J; Parshall B, 2003, 'Monomial bases for q-Schur algebras', Transactions of the American Mathematical Society, 355, pp. 1593 - 1620,
    Journal articles | 2003
    Du J, 2003, 'Finite-dimensional algebras and standard systems', Algebras and Representation Theory, 6, pp. 461 - 474
    Journal articles | 2002
    Du J; Parshall B, 2002, 'Linear quivers and the geometric setting of quantum GLn', Indagationes Mathematicae - New Series, 13, pp. 459 - 481
    Journal articles | 2001
    Du J; Rui H, 2001, 'Specht modules for ariki-koike algebras', Communications in Algebra, pp. 4701 - 4719
    Journal articles | 2000
    Du J; Rui H, 2000, 'Ariki-Koike algebras with semisimple bottoms', Mathematische Zeitschrift, pp. 807 - 830
    Journal articles | 2000
    Du J; Scott LM, 2000, 'The q-Schur2 algebras', Transactions of the American Mathematical Society, pp. 4325 - 4353
    Journal articles | 1999
    Du J; Rui H, 1999, 'Borel type subalgebras of the q-Schur m algebra', Journal of Algebra, pp. 567 - 595
    Journal articles | 1999
    Du J, 1999, 'A new proof for the canonical bases of type A', Algebra Colloquium, 6, pp. 377 - 383
    Journal articles | 1998
    Du J; Parshall B; Scott LM, 1998, 'Cells and q-Schur algebras', Transformation Groups, pp. 33 - 49
    Journal articles | 1998
    Du J; Parshall B; Scott LM, 1998, 'Quantum Weyl reciprocity and tilting modules', Communications in Mathematical Physics, 195, pp. 321 - 352
    Journal articles | 1998
    Du J; Parshall B; Scott LM, 1998, 'Stratifying endomorphism algebras associated to Hecke algebras', Journal of Algebra, 203, pp. 169 - 210
    Journal articles | 1998
    Du J; Rui H, 1998, 'Based algebras and standard bases for Quasi-Hereditary algebras', Transactions of the American Mathematical Society, pp. 3207 - 3235
    Journal articles | 1997
    Dipper R; Du J, 1997, 'Harish-Chandra vertices and Steinberg`s tensor product theorems for finite general linear groups', Proceedings of the London Mathematical Society, 3rd Series, 75, pp. 559 - 599,
    Journal articles | 1996
    Du J, 1996, 'Cells in certain sets of matrices', Tohoku Mathematical Journal, 48, pp. 417 - 427,
    Journal articles | 1996
    Du J, 1996, 'Global IC bases for quantum linear groups', Journal of Pure and Applied Algebra, 114, pp. 25 - 37,
    Journal articles | 1995
    Du J, 1995, 'A note on quantized Weyl reciprocity at roots of unity', Algebra Colloquium, 2, pp. 363 - 372
    Journal articles | 1995
    Du J, 1995, 'Canonical bases for irreducible representations of quantum GLn, II', Journal of the London Mathematical Society - Second Series, 51, pp. 461 - 470,
    Journal articles | 1995
    Du J, 1995, 'Q-Schur algebras, asymptotic forms and quantum SLn', Journal of Algebra, 177, pp. 385 - 408,
    Journal articles | 1994
    Du J; Scott L, 1994, 'Lusztig conjectures, old and new, I', Journal fur die Reine und Angewandte Mathematik, 1994, pp. 141 - 182,
    Journal articles | 1993
    Dipper R; Du J, 1993, 'Harish-Chandra vertices', Journal fur die Reine und Angewandte Mathematik, 1993, pp. 101 - 130,
    Journal articles | 1993
    Dipper R; Du J, 1993, 'Trivial and Alternating Source Modules of Hecke Algebras of Type A', Proceedings of the London Mathematical Society, s3-66, pp. 479 - 506,
    Journal articles | 1992
    Du J; Du J, 1992, 'The green correspondence for the representations of hecke algebras of type Ar-1', Transactions of the American Mathematical Society, 329, pp. 273 - 287,
    Journal articles | 1992
    Du J; Du J, 1992, 'The modular representation theory of q-schur algebras', Transactions of the American Mathematical Society, 329, pp. 253 - 271,
    Journal articles | 1992
    Du J, 1992, 'Canonical bases for irreducible representations of quantum GLn', Bulletin of the London Mathematical Society, 24, pp. 325 - 334,
    Journal articles | 1992
    Du J, 1992, 'Integral Schur algebras for GL 2', Manuscripta Mathematica, 75, pp. 411 - 427,
    Journal articles | 1991
    Du J; Wang JP, 1991, 'Two-parameter quantum linear groups and the hyperbolic invariance of q-schur algebras', Journal of the London Mathematical Society, s2-44, pp. 420 - 436,
    Journal articles | 1991
    Du J, 1991, 'The modular representation theory of q-Schur algebras. II', Mathematische Zeitschrift, 208, pp. 503 - 536,
  • Conference Papers | 2024
    Du J; Gu H; Zhou Z, 2024, 'Canonical bases for the modified quantum glm', in Proceedings of Symposia in Pure Mathematics, pp. 127 - 157,
    Conference Papers | 2024
    Du J; Parshall B; Scott L, 2024, 'An exact category approach to Hecke endomorphism algebras', in Proceedings of Symposia in Pure Mathematics, pp. 159 - 291,
    Conference Papers | 2016
    Du J, 2016, 'Structure and representations of the quantum loop algebra', in Proceedings of The 7th International Congress of Chinese Mathematicians, Beijing, China, presented at 7th International Congress of Chinese Mathematicians, Beijing, China, 06 April 2016 - 11 August 2016
    Conference Papers | 2011
    Du J, 2011, 'Structure and representations of affine q-Schur algebras', in Proceedings of Symposia in Pure Mathematics, Vol 86, American Mathematical Society, University of Virginia, pp. 137 - 158, presented at Southeastern Lie Theory Workshop: Finite and Algebraic Groups, University of Virginia, 01 June 2011 - 04 June 2011
    Conference Papers | 2010
    Deng B; Du J; Mah A, 2010, 'Generic extensions and composition monoids of cyclic quivers', in Chari V; Greenstein J; Misra KC; Raghavan KN; Viswanath S (eds.), Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory, American Mathematical Society, Bangalore, India, pp. 99 - 114, presented at International Congress of Mathematicians Satellite Conference Algebraic and Combinatorial Approaches to Represenation Theory, Bangalore, India, 12 August 2010 - 16 August 2010
    Conference Papers | 2004
    Du J; Rui H, 2004, 'Multi-parameter cells of finite Coxeter groups', in International Conference on Complex Geometry and Related Fields, International Conference on Complex Geometry and Related Fields, Shanghai, presented at International Conference on Complex Geometry and Related Fields, Shanghai
    Conference Papers | 2002
    Du J, 2002, 'Finite Dimensional Algebras, Quantum Groups and Finite Groups of Lie Type', in Fields Institute Communications, Fields Institute Communications, Toronto, USA, presented at Fields Institute Communications, Toronto, USA
    Conference Papers | 1998
    Du J; Scott LM, 1998, 'Stratifying q-Schur algebras', in international conference on representation theory, international conference on representation theory, Shanghai, China, presented at international conference on representation theory, Shanghai, China, 29 June 1998 - 03 July 1998
    Conference Papers | 1998
    Du J, 1998, 'Generalised q-Schur algebras and the ways to approach them', in Collins MJ; Parshall BJ; Scott LL (eds.), A symposium held at the University of Virginia, WALTER DE GRUYTER GMBH, Virginia, pp. 189 - 210, presented at a symposium held at the University of Virginia, Virginia, 08 May 1998 - 15 May 1998,