Pieri algebras for the orthogonal and symplectic groups

Abstract

We study the structure of a family of algebras which encodes a generalization of the Pieri Rule for the complex orthogonal group. In particular, we show that each of these algebras has a standard monomial basis and has a flat deformation to a Hibi algebra. There is also a parallel theory for the complex symplectic group.

26 pages, v2: new introduction, improved exposition, examples.

References in corpus (1)

• Reciprocity Algebras and Branching for Classical Symmetric Pairs

Cited by in corpus (2)

• Distributive Lattices, Affine Semigroups, and Branching Rules of the Classical Groups
• The nullcone in the multi-vector representation of the symplectic group and related combinatorics