| Abstract: Let $ G $ be a reductive algebraic group. Steinberg established a map
from the Weyl group to nilpotent $ G $-orbits using moment maps on
double flag varieties. In particular, in the case of the general
linear group, he re-interpreted the Robinson-Schensted correspondence,
which is combinatorial in its nature, in terms of the geometry of
complete flags. We generalize Steinberg's theory to the case of symmetric pairs $ (G,
K) $, and obtained two maps. They are called a "generalized Steinberg
map" and an "exotic moment map". We explain what they are like and
also discuss combinatorics related to them, which eventually lead to
two generalizations of the Robinson-Schensted correspondence. This is an on-going joint work with Lucas Fresse (IECL, University of
Lorraine). |