Two boundary Hecke Algebras and the combinatorics of type $C$

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Last updated: 27 January 2015

Contents

1	Introduction
2	The two-boundary Hecke algebra 2.1 The two-boundary braid group 2.2 The two-boundary Hecke algebra $H_k^{\text{ext}}$ 2.3 Weights of representations and intertwiners
3	Calibrated representations of $H_k^{\text{ext}}$ 3.1 Local regions 3.2 Classifying and constructing calibrated representations
4	Classification of irreducible representations of $H_2$ 4.1 Classification of central characters 4.2 Construction of the irreducible $H_2\text{-modules}$
5	Representations of ${ℬ}_k^{\text{ext}}$ in tensor space 5.1 Quantum groups and $R\text{-matrices}$ 5.2 The ${ℬ}_k^{\text{ext}}\text{-modules}$ $B_k^{\lambda }$ 5.3 Some tensor products for $𝔤={𝔤𝔩}_n$ 5.4 Irreducible $H_k^{\text{ext}}\text{-modules}$ in $M\otimes N\otimes V^{\otimes k}$

Notes and References

This is an excerpt from the paper Two boundary Hecke Algebras and the combinatorics of type $C$ Zajj Daugherty (Department of Mathematics, The City College of New York, NAC 8/133, Convent Ave at 138th Street, New York, NY 10031) and Arun Ram (Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010, Australia).

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