Conference abstracts

Session S08 - Lie Groups and Representations

July 29, 18:10 ~ 18:30

## Gröbner bases for local Weyl modules for generalized current $\mathfrak{sl}_2$-algebras

### Angelo Bianchi

### Federal University of São Paulo - UNIFESP, Brazil - acbianchi@unifesp.br

We use the theory of Gröbner bases for ideals to construct linear bases for the local Weyl modules for a generalized current algebra $\mathfrak{sl}_2\otimes_\mathbb C \mathbb C[t_1,\dots,t_n]$ associated to the finite-dimensional complex simple Lie algebra $\mathfrak{sl}_2$ and the polynomial algebra $\mathbb C[t_1,\dots,t_n]$ with $n=1,2,3$.

The main result is an explicit construction of linear bases for these important families of modules. In particular, we obtain some formulas to express the dimension of such modules. It is related to some works of Chari-Loktev, Chari-Pressley, Feigin-Loktev, and Loktev.