Realization of ${\bm B}_{\bm 2}$ type finite W-algebras
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摘要: 具体构造了\,$B_{2}$\,型李代数在所有幂零轨道下对应的有限\,W-代数的生成元集, 并通过计算得出了生成元之间的关系式, 从而给出了\,$B_{2}$\,型有限\,W-代数的具体实现.
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关键词:
- $B_{2}$~型李代数 /
- 非线性李代数 /
- Kazhdan\,滤过 /
- 有限W-代数
Abstract: In this paper we constructed an explicit set of generators for the finite W-algebras associated to all nilpotent orbits of $B_{2}$ type Lie algebras. We also computed the relations for these generators. The results give realization of $B_{2}$ type finite W-algebras. -
[1] {1} KOSTANT B. On Whittaker modules and representation theory[J]. Invent Math, 1978, 48: 101-184.{2} LYNCH T E. Generalized Whittaker vectors and representation theory[D]. Cambridge: MIT, 1979.{3} DE BOER J, TJIN T. Quantization and representation theory of finite W-algebras[J]. commun Math Phys, 1993, 158: 485-516.{4} PREMENT A. Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture[J]. Invent Math, 1995, 121: 79-117.{5} PREMENT A. Special transverse slices and their enveloping algebras[J]. Advances in Mathematics, 2002, 170:~1-55.{6} GINZBURG V.~Harish-Chandra bimodules for quantized Slodowy slices[J/OL]. Represent Theory, 2009, 13: 236-371.{7} PREMENT A. Commutative quotients of finite W-algebras[J]. Advances in Mathematics, 2010, 225:~269-306.{8} BRUNDAN J, KLESHCHEV A. Schur-Weyl duality for higher levels[J]. Selecta Math, 2008, 14:~1-57.{9} DE SOLE A, KAC V G. Finite vs affine W-algebras[J]. Japan J Math, 2006, 1: 137-261.{10} LOSEV I. Finite W-algebras[J/OL]. ICM talk 2010. arXiv:1003.5811.{11} BRUNDAN J, KLESHCHEV A. Shifted Yangians and finite W-algebras[J].~Advances in Mathematics,~2006, 200:~136-195.{12} BROWN J. Twisted Yangians and finite W-algebras[J]. Transform Groups, 2009, 14: 87-114.{13} GOODWIN S M, R\"{O}HRLE G, UBLY G. On 1-dimensional representations of finite W-algebras associated to simple Lie algebras of exceptional type[J/OL]. arXiv: 0905.3714v2, 2009.{14} BRUNDAN J, GOODWIN S M, KLESHCHEV A. Highest weight theory for finite W-algebras[J]. Internat Math Res Notices, 2008, 15, Art. ID rnn051.{15} GAN W L, GINZBURG V. Quantization of Slodowy slices[J]. Internat Math Res Notices, 2002(5): 243-255.{16} WANG W. Nilpotent orbits and W-algebras[J/OL]. arXiv: 0912.0689, 2009.{17} JANTZEN J C. Nilpotent orbits in representation theory[M]. Progress in Math 228. [S.L.]: Birkh\"{a}user, 2004.{18} CLARKE M C. Computing nilpotent and unipotent canonical forms:~A symmetric approach[J/OL]. arXiv: 1004.1116, 2010.{19} PREMET A. Enveloping algebras of Slodowy slices and the Joseph ideal[J]. J Eur Math Soc, 2007(9): 487-543.{20} BRUNDAND J, GOODWIN S M. Good grading polytopes[J]. Proc London Math Soc, 2007, 94: 155-180.{21} HUMPHREYS J E. Introduction to Lie algebras and representation theory[M]. New York: Springer-Verlag, 1972.{22} PREMET A. Primitive ideals, non-restricted representations and finite W-algebras[J]. Mosc Math J, 2007(7): 743-762.
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