A basis for the symplectic group branching algebra

Kim, Sangjib and Yacobi, Oded (2012) A basis for the symplectic group branching algebra. Journal of Algebraic Combinatorics, 35 2: 269-290.


Author Kim, Sangjib
Yacobi, Oded
Title A basis for the symplectic group branching algebra
Journal name Journal of Algebraic Combinatorics   Check publisher's open access policy
ISSN 0925-9899
1572-9192
Publication date 2012-03
Year available 2011
Sub-type Article (original research)
DOI 10.1007/s10801-011-0303-7
Volume 35
Issue 2
Start page 269
End page 290
Total pages 22
Place of publication New York, United States
Publisher Springer
Collection year 2012
Language eng
Formatted abstract The symplectic group branching algebra, ß, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n−2(ℂ) in each finite-dimensional irreducible representation of Sp2n (ℂ). By describing on ß an ASL structure, we construct an explicit standard monomial basis of ß consisting of Sp2n−2(ℂ) highest weight vectors. Moreover, ß is known to carry a canonical action of the n-fold product SL2×⋯×SL2, and we show that the standard monomial basis is the unique (up to scalar) weight basis associated to this representation. Finally, using the theory of Hibi algebras we describe a deformation of Spec(ß) into an explicitly described toric variety.
Keyword Symplectic groups
Branching rules
Hibi algebra
Algebra with straightening law
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online: 23 July 2011

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
 
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