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## 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. document.getElementById('cloak29a74967b1bdf5a82debbcfdca1e3f1f').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy29a74967b1bdf5a82debbcfdca1e3f1f = 'v&#97;n&#117;s&#97;mdyl&#101;wsk&#105;' + '&#64;'; addy29a74967b1bdf5a82debbcfdca1e3f1f = addy29a74967b1bdf5a82debbcfdca1e3f1f + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text29a74967b1bdf5a82debbcfdca1e3f1f = 'v&#97;n&#117;s&#97;mdyl&#101;wsk&#105;' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak29a74967b1bdf5a82debbcfdca1e3f1f').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy29a74967b1bdf5a82debbcfdca1e3f1f + '\'>'+addy_text29a74967b1bdf5a82debbcfdca1e3f1f+'<\/a>';

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).