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Abstract
We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules D λ, labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra RΛ0n over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde, p (λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of D λ. In particular, we prove that the q-character of D λ can be described in terms of DStde, p (λ). We show that a certain natural approach to constructing a basis of an arbitrary D λ does not work in general, giving a counterexample to a conjecture of Mathas.
Original language | English |
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Pages (from-to) | 631-669 |
Journal | Transformation Groups |
Volume | 23 |
Issue number | 3 |
Early online date | 19 Oct 2017 |
DOIs | |
Publication status | E-pub ahead of print - 19 Oct 2017 |
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Dive into the research topics of 'ON BASES OF SOME SIMPLE MODULES OF SYMMETRIC GROUPS AND HECKE ALGEBRAS'. Together they form a unique fingerprint.Projects
- 1 Finished
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Graded representations of symmetric groups and related algebras
Evseev, A.
Engineering & Physical Science Research Council
1/09/14 → 31/08/16
Project: Research Councils