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Session S16 - Quantum symmetries

No date set.

On the combinatorial rank of quantum groups

Vanusa Moreira Dylewksi

Universidade Federal do Rio Grande do Sul, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this work we present the definition of combinatorial rank and the first examples obtained by Kharchenko and collaborators, who calculated the combinatorial rank of the positive part $u_q^+(\mathfrak{g})$ of the multi-parameter version of the Lusztig quantum group, where $q$ is a root of the unity and $\mathfrak{g}$ is a simple Lie algebra of type $A_n$, $B_n$, $C_n$ and $D_n$. As a continuation of this study, we provide the combinatorial rank for quantum groups of type $G_2$ and $F_4$.

Joint work with Bárbara Pogorelsky(Universidade Federal do Rio Grande do Sul, Brazil) and Carolina Renz(Universidade Federal de Ciências da Saúde de Porto Alegre, Brazil).

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