Symmetric Functions and the Fock Space
作者： Bernard Leclerc
DOI: 10.1007/978-94-010-0524-1_4
关键词: Macdonald polynomials 、 Mathematics 、 Connection (mathematics) 、 Quantum affine algebra 、 Algebra 、 Fock space 、 Standard basis 、 Kazhdan–Lusztig polynomial 、 Representation (mathematics) 、 Pure mathematics 、 Symmetric function
摘要: We review the definition, calculation and properties of canonical bases Fock space representation . emphasize close connection with theory symmetric functions (plethysm, Hall-Littlewood functions, Macdonald polynomials)
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sci-hub.st 参考文章(41)
I. B. Frenkel, Representations of affine lie algebras, hecke modular forms and korteweg—De vries type equations Springer, Berlin, Heidelberg. pp. 71- 110 ,(1982) , 10.1007/BFB0093354
V. G. Drinfeld, Hopf algebra and Yang-Baxter equation Soviet Math. Dokl.. ,vol. 32, pp. 254- 258 ,(1985)
Hyoue Miyachi, Akihiko Hida, ON THE PRINCIPAL BLOCKS OF FINITE GENERAL LINEAR GROUPS IN NON-DEFINING CHARACTERISTIC (Cohomology theory of finite groups) 京都大学数理解析研究所. ,(2000)
Kouichi Takemura, Denis Uglov, Representations of the Quantum Toroidal Algebra on Highest Weight Modules of the Quantum Affine Algebra of Type \mathfrak{gl} N Publications of The Research Institute for Mathematical Sciences. ,vol. 35, pp. 407- 450 ,(1999) , 10.2977/PRIMS/1195143609
Gordon James, Adalbert Kerber, The representation theory of the symmetric group Cambridge University Press. ,(1984) , 10.1017/CBO9781107340732
Susumu Ariki, On the decomposition numbers of the Hecke algebra of $G(m, 1, n)$ Journal of Mathematics of Kyoto University. ,vol. 36, pp. 789- 808 ,(1996) , 10.1215/KJM/1250518452
George Lusztig, Introduction to Quantum Groups ,(1993)
Christophe Carré, Bernard Leclerc, Splitting the Square of a Schur Function into its Symmetric and Antisymmetric Parts Journal of Algebraic Combinatorics. ,vol. 4, pp. 201- 231 ,(1995) , 10.1023/A:1022475927626
V. G. DRINFEL'D, Hopf algebras and the quantum Yang-Baxter equation Proceedings of the USSR Academy of Sciences. ,vol. 32, pp. 254- 258 ,(1985) , 10.1142/9789812798336_0013
Victor G. Kac, Infinite-Dimensional Lie Algebras idla. pp. 422- ,(1990) , 10.1017/CBO9780511626234