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A Remark on BMW algebra, $q$-Schur Algebras and Categorification

  Published:2013-08-10
 Printed: Apr 2014
  • Pedro Vaz,
    CAMGSD, Instituto Superior Técnico , Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
  • Emmanuel Wagner,
    Institut de Mathématiques de Bourgogne UMR 5584 du CNRS, 7 avenue Alain Savary BP 47870 21078 Dijon Cedex, France
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Abstract

We prove that the 2-variable BMW algebra embeds into an algebra constructed from the HOMFLY-PT polynomial. We also prove that the $\mathfrak{so}_{2N}$-BMW algebra embeds in the $q$-Schur algebra of type $A$. We use these results to suggest a schema providing categorifications of the $\mathfrak{so}_{2N}$-BMW algebra.
Keywords: tangle algebras, BMW algebra, HOMFLY-PT Skein algebra, q-Schur algebra, categorification tangle algebras, BMW algebra, HOMFLY-PT Skein algebra, q-Schur algebra, categorification
MSC Classifications: 57M27, 81R50, 17B37, 16W99 show english descriptions Invariants of knots and 3-manifolds
Quantum groups and related algebraic methods [See also 16T20, 17B37]
Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
None of the above, but in this section
57M27 - Invariants of knots and 3-manifolds
81R50 - Quantum groups and related algebraic methods [See also 16T20, 17B37]
17B37 - Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
16W99 - None of the above, but in this section
 

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