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TILING BRANCHING MULTIPLICITY SPACES WITH GL${}_{2} $ PATTERN BLOCKS

Part of: Algebraic combinatorics Linear algebraic groups and related topics

Published online by Cambridge University Press:  10 April 2013

SANGJIB KIM
SANGJIB KIM*
Affiliation:
Department of Mathematics, Ewha Womens University, Seoul 120-750, South Korea
*
[email protected]
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Abstract

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We study branching multiplicity spaces of complex classical groups in terms of ${\mathrm{GL} }_{2} $ representations. In particular, we show how combinatorics of ${\mathrm{GL} }_{2} $ representations are intertwined to make branching rules under the restriction of ${\mathrm{GL} }_{n} $ to ${\mathrm{GL} }_{n- 2} $. We also discuss analogous results for the symplectic and orthogonal groups.

Keywords

classical groupsrepresentationsbranching rules

MSC classification

Secondary: 20G05: Representation theory 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 94 , Issue 3 , June 2013 , pp. 362 - 374
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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