Geodesic
A basis for the symplectic group branching algebra
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 2, pp. 269-290.

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Summary: The symplectic group branching algebra, $B \mathcal $B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp $_{2 n - 2}(\Bbb C)$ in each finite-dimensional irreducible representation of Sp $_{2 n }(\Bbb C)$. By describing on $B \mathcal $B an ASL structure, we construct an explicit standard monomial basis of $B \mathcal $B consisting of Sp $_{2 n - 2}(\Bbb C)$ highest weight vectors. Moreover, $B \mathcal $B is known to carry a canonical action of the $n$-fold product SL $_{2}\times \dots \times $SL $_{2}$, 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 $Spec( B)$ mathrmSpec($\mathcal $B) into an explicitly described toric variety.
Keywords: keywords symplectic groups, branching rules, hibi algebra, algebra with straightening law 
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     author = {Kim, Sangjib and Yacobi, Oded},
     title = {A basis for the symplectic group branching algebra},
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     pages = {269--290},
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     volume = {35},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__35_2_a2/}
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Kim, Sangjib; Yacobi, Oded. A basis for the symplectic group branching algebra. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 2, pp. 269-290. http://geodesic.mathdoc.fr/item/JAC_2012__35_2_a2/