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 Hkext
2.3 Weights of representations and intertwiners
3 Calibrated representations of Hkext
3.1 Local regions
3.2 Classifying and constructing calibrated representations
4 Classification of irreducible representations of H2
4.1 Classification of central characters
4.2 Construction of the irreducible H2-modules
5 Representations of kext in tensor space
5.1 Quantum groups and R-matrices
5.2 The kext-modules Bkλ
5.3 Some tensor products for 𝔤=𝔤𝔩n
5.4 Irreducible Hkext-modules in MNVk

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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