MathematicsSeminar |
Rocky Mountain Algebraic Combinatorics Seminar
Upcoming Seminars Schedule
Constructive Membership Tests in Some Infinite Matrix Groups
Alexander Hulpke
Colorado State University
We describe algorithms and heuristics that allow us to express arbitrary elements of SLn(Z) and Sp2n(Z) as products of generators in particular "standard" generating sets. For elements obtained experimentally as random products, it produces product expressions whose lengths are competitive with the input lengths.
Subregular $J$-rings of Coxeter systems as quotients of path algebras
Tianjuan Xu
University of Colorado, Boulder
The asymptotic Hecke algebra, or J-ring, of a Coxeter system is an associative algebra closely related to the Hecke algebra of the system. We study a subalgebra JC of J which has a natural basis indexed by the rigid elements of the Coxeter group, where “rigid" means having a unique reduced word. Exploiting the rigidity property, we show that JC can be realized as a certain quotient of the path algebra of the double quiver of the Coxeter diagram of the system. This allows us to use quiver representations to answer representation-theoretical questions about JC, such as when JC is semisimple, in terms of graph-theoretical properties of the Coxeter diagram.
Weber 223
4–6 pm
Friday, Sep 27, 2019
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University
This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.