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A GENERIC MULTIPLICATION IN QUANTIZED SCHUR ALGEBRAS.
- Source :
- Quarterly Journal of Mathematics; Dec2010, Vol. 61 Issue 4, p497-510, 14p
- Publication Year :
- 2010
-
Abstract
- We define a generic multiplication in quantized Schur algebras and thus obtain a new algebra structure in the Schur algebras. We prove that via a modified version of the map from quantum groups to quantized Schur algebras, defined in (A. A. Beilinson, G. Lusztig and R. MacPherson, A geometric setting for the quantum deformation of GLn, Duke Math. J. 61 (1990), 655–677), a subalgebra of this new algebra is a quotient of the monoid algebra in Hall algebras studied in (M. Reineke, Generic extensions and multiplicative bases of quantum groups at q = 0, Represent. Theory 5 (2001), 147–163). We also prove that the subalgebra of the new algebra gives a geometric realization of a positive part of 0-Schur algebras, defined in (S. Donkin, The q-Schur Algebra, London Mathematical Society Lecture Note Series 253. Cambridge University Press, Cambridge, 1998, x + 179. ISBN: 0-521-64558-1.). Consequently, we obtain a multiplicative basis for the positive part of 0-Schur algebras. [ABSTRACT FROM PUBLISHER]
- Subjects :
- MULTIPLICATION
ALGEBRA
SCHUR functions
GEOMETRY
QUANTUM groups
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00335606
- Volume :
- 61
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Quarterly Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 55117890
- Full Text :
- https://doi.org/10.1093/qmath/hap016