Descent representations and multivariate statistics

By R. Adin, Francesco Brenti, Yuval Roichman. 2001

67 citations recorded by the source corpus.

Combinatorial identities on Weyl groups of types A and B are derived from special bases of the corresponding coinvariant algebras. Using the Garsia-Stanton descent basis of the coinvariant algebra of type A we give a new construction of the Solomon descent representations. An extension of the descent basis to type B, using new multivariate statistics on the group, yields a refinement of the descent representations. These constructions are then applied to refine well-known decomposition rules of the coinvariant algebra and to generalize various identities.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ecaffb384b6df58a23cb5b9974b63f97c9ac4dd6

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In Discrete Mathematics and Combinatorics

1. James Haglund
2. Mark Shimozono
3. Brendon Rhoades
4. E. Gorsky
5. Thomas Lam
6. Mike Zabrocki
7. Sarah K. Mason

In Geometry and Topology

1. James Haglund
2. Mark Shimozono
3. Brendon Rhoades
4. Thomas Lam

In Mathematical Physics

1. James Haglund
2. Mark Shimozono
3. Brendon Rhoades

Citations in the corpus

• Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture (2016, methodology): “[n]q := 1 + q + · · ·+ q n−1 [n]!q := [n]q[n− 1]q · · · [1]q [ n a1, .”