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 twoboundary Hecke algebra
2.1 
The twoboundary braid group

2.2 
The twoboundary 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 ${\mathcal{B}}_{k}^{\text{ext}}$ in tensor space
5.1 
Quantum groups and $R\text{matrices}$

5.2 
The ${\mathcal{B}}_{k}^{\text{ext}}\text{modules}$ ${B}_{k}^{\lambda}$

5.3 
Some tensor products for $\U0001d524={\U0001d524\U0001d529}_{n}$

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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