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SUMMARY:Ashish Mishra (Universidade Federal do Pará\, Belém)
DTSTART:20220303T100000Z
DTEND:20220303T110000Z
DTSTAMP:20260423T024447Z
UID:ARCSIN/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ARCSIN/16/">
 The Jucys--Murphy elements</a>\nby Ashish Mishra (Universidade Federal do 
 Pará\, Belém) as part of ARCSIN - Algebra\, Representations\, Combinator
 ics and Symmetric functions in INdia\n\n\nAbstract\nThe representation the
 ory of a multiplicity free tower of finite-dimensional semisimple associat
 ive algebras is determined by the actions of Jucys--Murphy elements. These
  elements were  discovered independently by Jucys and Murphy for the symme
 tric groups\, and later on\, these elements  played an important role in t
 he development of spectral approach to the representation theory of symmet
 ric groups given by Okounkov and Vershik. The motivation for the spectral 
 approach comes from the work of Gelfand and Tsetlin on the irreducible fin
 ite-dimensional modules of general linear Lie algebras. \n\nAfter a brief 
 description of the history and fundamental properties of Jucys--Murphy ele
 ments\, our main objective in this seminar is to describe these elements a
 nd to study their applications in the representation theory of following a
 lgebras: (i) partition algebras for complex reflection groups\, (ii) rook 
 monoid algebras\, and (iii) totally propagating partition algebras. The re
 sults presented in this seminar are joint work with Dr. Shraddha Srivastav
 a.\n
LOCATION:https://researchseminars.org/talk/ARCSIN/16/
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