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SUMMARY:Elitza Hristova (Institute of Mathematics and Informatics\, Bulgar
 ia)
DTSTART:20230828T150000Z
DTEND:20230828T160000Z
DTSTAMP:20260423T021120Z
UID:ENAAS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/30/">O
 n the GL(n)-module structure of Lie nilpotent associative relatively free 
 algebras</a>\nby Elitza Hristova (Institute of Mathematics and Informatics
 \, Bulgaria) as part of European Non-Associative Algebra Seminar\n\n\nAbst
 ract\nLet $K\\langle X\\rangle$ denote the free associative algebra genera
 ted by a finite set $X$ with n elements over a field $K$ of characteristic
  0. Let $I_p$ denote the two-sided associative ideal in $K\\langle X\\rang
 le$ generated by all commutators of length $p$\, where $p$ is an arbitrary
  positive integer greater than 1. The group ${\\rm GL(n)}$ acts in a natur
 al way on the quotient $K\\langle X\\rangle/I_p$ and the ${\\rm GL(n)}$-mo
 dule structure of $K\\langle X\\rangle/I_p$ is known for $p=2\,3\,4\,5$. I
 n this talk\, we give some results on the ${\\rm GL}(n)$-module structure 
 of $K\\langle X\\rangle/I_p$ for any $p$. More precisely\, we give a bound
  on the values of the highest weights of irreducible ${\\rm GL}(n)$-module
 s which appear in the decomposition of $K\\langle X\\rangle/I_p$. We discu
 ss also applications of these results related to the algebras of G-invaria
 nts in $K\\langle X\\rangle/I_p$\, where G is one of the classical ${\\rm 
 GL}(n)$-subgroups ${\\rm SL}(n)$\, ${\\rm O}(n)$\, ${\\rm SO}(n)$\, or ${\
 \rm Sp}(2k)$ (for $n=2k$).\n
LOCATION:https://researchseminars.org/talk/ENAAS/30/
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