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


Published:20130810
Printed: Apr 2014
Pedro Vaz,
CAMGSD, Instituto Superior Técnico , Avenida Rovisco Pais, 1049001 Lisboa, Portugal
Emmanuel Wagner,
Institut de Mathématiques de Bourgogne UMR 5584 du CNRS, 7 avenue Alain Savary BP 47870 21078 Dijon Cedex, France
Abstract
We prove that the 2variable BMW algebra
embeds into an algebra constructed from the HOMFLYPT 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.
MSC Classifications: 
57M27, 81R50, 17B37, 16W99 show english descriptions
Invariants of knots and 3manifolds 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 3manifolds 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
