Affine and degenerate affine BMW algebras: Actions on tensor space

Z Daugherty; A Ram; R Virk

Journal article

Affine and degenerate affine BMW algebras: Actions on tensor space

Z Daugherty, A Ram, R Virk

Selecta Mathematica New Series | Published : 2013

DOI: 10.1007/s00029-012-0105-3

Abstract

The affine and degenerate affine Birman-Murakami-Wenzl (BMW) algebras arise naturally in the context of Schur-Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively. Cyclotomic BMW algebras, affine and cyclotomic Hecke algebras, and their degenerate versions are quotients of the affine and degenerate affine BMW algebras. In this paper, we explain how the affine and degenerate affine BMW algebras are tantalizers (tensor power centralizer algebras) by defining actions of the affine braid group and the degenerate affine braid algebra on tensor space and showing that, in important cases, these actions induce actions of the affine and degenerate affine BMW algebr..

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University of Melbourne Researchers

Arun Ram Author

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Grants

Awarded by Australian Research Council

Funding Acknowledgements

Significant work on this paper was done while the authors were in residence at the Mathematical Sciences Research Institute (MSRI) in 2008. We thank MSRI for hospitality, support, and a wonderful working environment. We thank F. Goodman and A. Molev for their helpful comments and references. This research has been partially supported by the National Science Foundation DMS-0353038 and the Australian Research Council DP0986774 and DP120101942.