Geodesic
On the multiplication of spherical functions of reductive spherical pairs of type A
Canadian journal of mathematics, Tome 75 (2023) no. 2, pp. 341-374

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DOI

Let G be a simple complex algebraic group, and let $K \subset G$ be a reductive subgroup such that the coordinate ring of $G/K$ is a multiplicity-free G-module. We consider the G-algebra structure of $\mathbb C[G/K]$ and study the decomposition into irreducible summands of the product of irreducible G-submodules in $\mathbb C[G/K]$. When the spherical roots of $G/K$ generate a root system of type $\mathsf A$, we propose a conjectural decomposition rule, which relies on a conjecture of Stanley on the multiplication of Jack symmetric functions. With the exception of one case, we show that the rule holds true whenever the root system generated by the spherical roots of $G/K$ is a direct sum of subsystems of rank 1.
DOI : 10.4153/S0008414X21000651
Mots-clés : Reductive spherical pairs, multiplicity-free actions, coordinate rings of spherical varieties, Jack polynomials 
Bravi, Paolo; Gandini, Jacopo. On the multiplication of spherical functions of reductive spherical pairs of type A. Canadian journal of mathematics, Tome 75 (2023) no. 2, pp. 341-374. doi: 10.4153/S0008414X21000651
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     title = {On the multiplication of spherical functions of reductive spherical pairs of type {A}},
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     year = {2023},
     volume = {75},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000651/}
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