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Zbl 1130.20009
Yvonne, Xavier
A conjecture for $q$-decomposition matrices of cyclotomic $v$-Schur algebras. (English)
[J] J. Algebra 304, No. 1, 419-456 (2006). ISSN 0021-8693

The Jantzen sum formula for cyclotomic $v$-Schur algebras yields an identity for some $q$-analogues of the decomposition matrices of these algebras. In this paper, the author proves a similar identity for matrices of canonical bases of higher-level Fock spaces. Furthermore, the author proposes a conjecture which asserts that these matrices are actually identical for a suitable choice of parameters.
[Hu Jun (Beijing)]

MSC 2000:: *20C08 Hecke algebras and their representations
17B37 Quantum groups and related deformations
20C30 Representations of finite symmetric groups
81R50 Quantum groups and related algebraic methods in quantum theory

Keywords: cyclotomic Schur algebras; Weyl modules; Jantzen sum formula; canonical bases; decomposition matrices; Fock spaces

Cited in: Zbl 1223.17018

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