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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Combinatorial extension of stable branching rules for classical groups


Author: Jae-Hoon Kwon
Journal: Trans. Amer. Math. Soc. 370 (2018), 6125-6152
MSC (2010): Primary 17B37, 22E46, 05E10
DOI: https://doi.org/10.1090/tran/7104
Published electronically: February 1, 2018
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Abstract: We give new combinatorial formulas for decomposition of the tensor product of integrable highest weight modules over the classical Lie algebras of types $ B, C, D$, and the branching decomposition of an integrable highest weight module with respect to a maximal Levi subalgebra of type $ A$. This formula is based on a combinatorial model of classical crystals called spinor model. We show that our formulas extend in a bijective way various stable branching rules for classical groups to arbitrary highest weights, including the Littlewood restriction rules.


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Additional Information

Jae-Hoon Kwon
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea
Email: jaehoonkw@snu.ac.kr

DOI: https://doi.org/10.1090/tran/7104
Keywords: Branching rules, classical groups, quantum groups, crystal graphs
Received by editor(s): December 12, 2015
Received by editor(s) in revised form: October 1, 2016, and October 16, 2016
Published electronically: February 1, 2018
Additional Notes: This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1501-01.
Article copyright: © Copyright 2018 American Mathematical Society

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