Flag varieties over semifields

2021/01/28 木 10:30 - 12:00
Xuhua He
The Chinese University of Hong Kong

In 1994, Lusztig developed the theory of total positivity for
arbitrary split real reductive groups and their flag manifolds. Later
the theory has found important applications in different areas: cluster
algebras, higher Teichmuller theory, the theory of amplituhedron in
physics, etc.
Recently, Lusztig initiated the study of Kac-Moody monoids over
arbitrary semifield and their flag manifolds. In the case where the
Kac-Moody datum comes from a real reductive group and the semifield is
$\mathbb R_{>0}$, the Kac-Moody monoid over $\mathbb R_{>0}$ is exactly
the totally nonnegative part of the real reductive group.
In this talk, I will discuss my joint work with Huanchen Bao on the flag
manifolds $\mathcal B(K)$ over arbitrary semifield $K$ and associated to
any Kac-Moody? datum $G$. We show that $\mathcal B(K)$ admits a natural
action of the Kac-Moody monoid $G(K)$ and admits a decomposition into

NOTE: This is a zoom seminar, and

zoom URL: https://kyoto-u-edu.zoom.us/j/87521586296
passcode: The minimal dimension of the smallest non-trivial irreducible representation of the Monster group over $\mathbb C$