Matthew Fayers
An LLT-type algorithm for computing higher-level canonical bases.
Thu, 01/28/2010 - 16:01 — SomNambulAuthors: Matthew Fayers
Subjects: Quantum Algebra
AbstractWe give a fast algorithm for computing the canonical basis of an irreducible
highest-weight module for $U_q(\hat{\mathfrak{sl}}_e)$, generalising the LLT
algorithm.Partition models for the crystal of the basic $U_q(\hat{\mathfrak{sl}}_n)$-module.
Thu, 01/21/2010 - 16:01 — SomNambulAuthors: Matthew Fayers
Subjects: Combinatorics
AbstractFor each $n\geqslant3$, we construct an uncountable family of models of the
crystal of the basic $U_q(\hat{\mathfrak{sl}}_n)$-module. These models are all
based on partitions, and include the usual $n$-regular and $n$-restricted
models, as well as Berg's ladder crystal, as special cases.On the irreducible Specht modules for Iwahori--Hecke algebras of type A with $q=-1$.
Tue, 11/03/2009 - 16:01 — SomNambulAuthors: Matthew Fayers
Subjects: Representation Theory
AbstractLet $p$ be a prime and $\mathbb{F}$ a field of characteristic $p$, and let
$\mathcal{H}_n$ denote the Iwahori--Hecke algebra of the symmetric group
$\mathfrak{S}_n$ over $\mathbb{F}$ at $q=-1$. We prove that there are only
finitely many partitions $\lambda$ such that both $\lambda$ and $\lambda'$ are
2-singular and the Specht module $S^\lambda$ for $\mathcal{H}_{|\la|}$ is
irreducible.General runner removal and the Mullineux map.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Matthew Fayers
Subjects: Representation Theory
AbstractWe prove a new `runner removal theorem' for $q$-decomposition numbers of the
level 1 Fock space of type $A^{(1)}_{e-1}$, generalising earlier theorems of
James--Mathas and the author. By combining this with another theorem relating
to the Mullineux map, we show that the problem of finding all $q$-decomposition
numbers indexed by partitions of a given weight is a finite computation.
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