11 research outputs found
Schur elements for the Ariki-Koike algebra and applications
We study the Schur elements associated to the simple modules of the
Ariki-Koike algebra. We first give a cancellation-free formula for them so that
their factors can be easily read and programmed. We then study direct
applications of this result. We also complete the determination of the
canonical basic sets for cyclotomic Hecke algebras of type in
characteristic 0.Comment: The paper contains the results of arXiv:1101.146
The Symbolic and cancellation-free formulae for Schur elements
In this paper we give a symbolical formula and a cancellation-free formula
for the Schur elements associated to the simple modules of the degenerate
cyclotomic Hecke algebras. As some direct applications, we show that the Schur
elements are symmetric with respect to the natural symmetric group action and
are integral coefficients polynomials and we give a different proof of
Ariki-Mathas-Rui's criterion on the semi-simplicity of degenerate cyclotomic
Hecke algebras.Comment: To appear in Monatshefte fur Mathemati
An analogue of row removal for diagrammatic cherednik algebras
We prove an analogue of James–Donkin row removal theorems for diagrammatic
Cherednik algebras. This is one of the first results concerning the (graded) decomposition numbers
of these algebras over fields of arbitrary characteristic. As a special case, our results yield a new
reduction theorem for graded decomposition numbers and extension groups for cyclotomic q-Schur
algebras
A generalized skein relation for Khovanov homology and a categorification of the θ-invariant
The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are able to generalize the Khovanov homology in order to obtain a categorification of the θ-invariant, which is itself a generalization of the Jones polynomial. Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh