Alladi Ramakrishnan Hall

Schur-Weyl dualities and diagram algebras

T. Geetha

IMSc

In this talk we will discuss Schur-Weyl duality, the center
piece of representation theory which relates the combinatorial and
representation theories of general linear group and symmetric group. Its
classical version is due to Issai Schur (1901 and 1927) who studied this
in connection to the polynomial representations of general linear group
using the symmetric group. After Schur's work, several attempts have been
made to study the analogues of this duality. We will explore two important
class of algebras called "Schur algebras" and "diagram algebras" which
arise from this duality in connection to other theories like Lie theory,
quantum groups, statistical mechanics and mathematical physics. We will
see an overview of these class of algebras and my recent work in this
direction.