IMSc Webinar

The Jucys--Murphy elements

Ashish Mishra

Universidade Federal do Pará, Belém

This is a lecture in the ARCSIN seminar series:
researchseminars.org/seminar/ARCSIN
zoom link:
zoom.us/j/91288928049?pwd=WHNaUE9TZEdZWGR3aGNtN2JvWDNtZz09
password: Macdonald

The representation theory of a multiplicity free tower of finite-dimensional semisimple associative algebras is determined by the actions of Jucys--Murphy elements. These elements were discovered independently by Jucys and Murphy for the symmetric groups, and later on, these elements played an important role in the development of spectral approach to the representation theory of symmetric groups given by Okounkov and Vershik. The motivation for the spectral approach comes from the work of Gelfand and Tsetlin on the irreducible finite-dimensional modules of general linear Lie algebras.

After a brief description of the history and fundamental properties of Jucys--Murphy elements, our main objective in this seminar is to describe these elements and to study their applications in the representation theory of following algebras: (i) partition algebras for complex reflection groups, (ii) rook monoid algebras, and (iii) totally propagating partition algebras. The results presented in this seminar are joint work with Dr. Shraddha Srivastava.