## Permutations statistics, invariants and coinvariant algebra for the
Weyl group of type D.

### Riccardo Biagioli, (UQAM)

Abstract: There are several connections between permutation statistics on the
symmetric group and the representation theory of the symmetric group S_n.
After giving a brief survey of the known results for S_n, I will show how
to generalize them
to the even-signed permutation group D_n. In particular I will define a
major index and a descent number on D_n that
allow me to give an explicit formula for the Hilbert series for the
invariants of the diagonal action of D_n on the polynomial ring.
Moreover I will give a monomial basis for the coinvariant algebra R(D).
This new basis leads to
the definition of a new family of D_n modules that decompose R(D).
An explicit decomposition of these representations into irreducible
components is obtained by extending the major index on particular
standard Young bitableaux.

This is a joint work with Fabrizio Caselli.

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