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arXiv · 1403.7740

Decomposition numbers of quantized walled Brauer algebras

Hebing Rui·Linliang Song
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Abstract

In this paper, we establish explicit relationship between decomposition numbers of quantized walled Brauer algebras and those for either Hecke algebras associated to certain symmetric groups or (rational) $q$-Schur algebras over a field $\kappa$. This enables us to use Ariki's result \cite{Ar} and Varagnolo-Vasserot's result \cite{VV} to compute such decomposition numbers via inverse Kazhdan-Lusztig polynomials associated with affine Weyl groups of type $A$ if the ground field is $\mathbb C$.

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Hebing Rui, Linliang Song. 2014-03-30. Decomposition numbers of quantized walled Brauer algebras. https://arxiv.org/abs/1403.7740

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