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Infinitesimal quantum and little q-Schur algebras
- Source :
-
Journal of Algebra . May2005, Vol. 287 Issue 1, p199-233. 35p. - Publication Year :
- 2005
-
Abstract
- Abstract: We first follow De Concini and Kac [in: A. Connes, M. Dulfo, A. Joseph, R. Rentshler (Eds.), Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory, 1990, pp. 471–506] to give a presentation for the infinitesimal quantum , , and then reconstruct or realize in two different ways following the Beilinson–Lusztig–MacPherson geometric setting approach [Duke Math. J. 61 (1990) 655–677]. Thus, we obtain three new bases for . In the second part of the paper, we use to introduce the little q-Schur algebra as a subalgebra of the q-Schur algebra . The symmetry structure of a little q-Schur algebra is then investigated through the construction of various bases of monomial, BLM and PBW types for and q-Schur algebras. We also obtain a formula for the dimension of . [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*ALGEBRA
*MATHEMATICAL analysis
*OPERATOR theory
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 287
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 16901309
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2005.01.040