1. A descent basis for the coinvariant algebra of type D
- Author
-
Fabrizio Caselli, Riccardo Biagioli, F. Caselli, and R. Biagioli
- Subjects
Weyl group ,Algebra and Number Theory ,WEYL GROUP ,Coinvariant algebra ,Multiplicity (mathematics) ,Young tableaux ,Monomial basis ,DESCENT BASIS ,Algebra ,symbols.namesake ,Homogeneous ,Mathematics::Quantum Algebra ,symbols ,Young tableau ,Algebraic number ,Mathematics::Representation Theory ,DESCENT REPRESENTATIONS ,Permutation statistics ,Mathematics - Abstract
A monomial basis for the coinvariant algebra of type D is introduced. This basis naturally leads to the definition of a new family of representations that decompose the homogeneous components of the coinvariant algebra. Furthermore, the multiplicity of the irreducible characters within the characters of these representations is described in terms of tableaux. This algebraic setting is then applied to generalize various combinatorial identities and find new ones.
- Full Text
- View/download PDF