Seminar za teoriju reprezentacija ZCI QuantiXLie

PMF Matematički odsjek
14.06.2018 - 17:15 - 18:30
Representation theory seminar and Center of Excellence QuantiXLie
Thursday, June 14 at 17:15, room 002
Ivan Penkov: Representations of large matrix Lie algebras
Consider the Lie  algebra of infinite matrices each row and column of which are
finite. Is there a theory, for this Lie algebra, which can be considered an
analogue of the theory of finite-dimensional representations of sl(n)? The
answer is "yes" and I will construct a category of tensor modules for this Lie
algebra. The main point is that this category is not semisimple. It  is a Koszul
highest weight category, and I willI give a combinatorial formula for the Exts
between simple modules.
In the second part of the talk I will extend the construction to matrices
whose matrix positions form sets of arbitrary cardinality.
Everybody is invited.
Karmen Grizelj
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