A Remark on BMW Algebra, q-Schur Algebras and Categorification

Vaz, Pedro ; Wagner, Emmanuel

Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 453-480

Résumé

We prove that the two-variable $\text{BMW}$ algebra embeds into an algebra constructed from the $\text{HOMFLY-PT}$ polynomial. We also prove that the $\mathfrak{s}{{\mathfrak{O}}_{2N}}-\text{BMW}$ algebra embeds in the $q$ -Schur algebra of type $A$ . We use these results to suggest a schema providing categorifications of the $\mathfrak{s}{{\mathfrak{D}}_{2N}}-\text{BMW}$ algebra.

Détail

DOI : 10.4153/CJM-2013-018-1

Mots-clés : 57M27, 81R50, 17B37, 16W99, tangle algebras, BMW algebra, HOMFLY-PT Skein algebra, q-Schur algebra, categorification

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