About this Event
850 Polytechnic Lane, Marietta, GA 30060
#CSMDiscreteMathSpeaker: Dr. Mark Skandera, Lehigh University
Title: “Hecke algebra character evaluation and graph coloring”
Abstract: If $w$ in the symmetric group $S_n$ avoids the patterns $3412$ and $4231$, then we may graphically represent the Kazhdan-Lusztig basis element $\widetilde C_w(1) \in \mathbb Z[S_n]$ by a poset $P = P(w)$ or a graph $G = G(w)$. We may then compute the evaluations of certain $Z[S_n]$-characters at $\widetilde C_w(1)$ by decomposing $P$ into chains or by coloring $G$.
These results hold also for a certain q-deformation $H_n(q)$ of $Z[S_n]$ called the Hecke algebra. It, too, has a Kazhdan-Lusztig basis whose elements $\widetilde C_w(q)$ may be represented by the poset and graph above. We will show how to use the same chain decompositions and colorings above to evaluate $H_n(q)$-characters at $\widetilde C_w(q)$.
The Discrete Math Seminar (DMS) is intended for Kennesaw State faculty working in the various areas of algebra, number theory, and discrete mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone who is interested in attending. This talk will take place in a hybrid format – in-person in D-224 or virtually.
Dial-In Instructions
Passcode: 9TNQ7j
Passcode: 9TNQ7j
Call-in number (audio only): +1 470 648 2566