##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Jean-Christophe Aval

#### University of Bordeaux

## Invariant and coinvariant polynomials for the generalized symmetric groups

##### Abstract:

Symmetric polynomials are the invariants of the classical action of the symmetric group Sn on the space Q[Xn] of polynomials by permutation of the variables. It is well known that the dimension of the quotient of Q[Xn] by the ideal generated by symmetric, constant-free polynomials is n!. When we consider other actions or other groups, we have different spaces of invariants, and different quotients (coinvariants). We will discuss some examples, in particular quasi-symmetrizing actions, whose coinvariants have dimensions given by the Catalan numbers. We shall give explicit Grobner bases for the ideals generated by the invariants .

Host: Adriano Garsia

### March 11, 2003

### 3:00 PM

### AP&M 7321

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