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A Remark on BMW Algebra, q-Schur Algebras and Categorification
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- Journal:
- Canadian Journal of Mathematics / Volume 66 / Issue 2 / 01 April 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 453-480
- Print publication:
- 01 April 2014
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- Article
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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.
