| Thu, Feb 13, 2025
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Combinatorial and Commutative Algebra Seminar
4:00 PM
MSCS 514 | | Folding subgroups of Coxeter groups I
Camilo Villamil Chalarca, OSU
| | | Abstract: Consider a Coxeter system $(W, S)$ with Coxeter graph $\Gamma$. Let $\sigma$ be an automorphism on $\Gamma$, which extends to an automorphism on the Coxeter group $W$ that preserves length. Then $\sigma$ defines a partition on $S$, and such a partition provides a Coxeter system $(W_F, R)$ where $W_F$ is the subgroup of $W$ fixed by $\sigma$. We call $W_F$ the folding subgroup of $W$. In this first talk, we will describe the folding process when $W$ is a Coxeter group of type $A_{2n-1}$, $n\geq 2$, or of type $D_{n+1}$, $n\geq 3$. We will present some results, conjectures, and open questions on the distribution of the elements of $W_F$ inside $W$ and the structure of the quotient $W/W_F$. |
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