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Gregg
Zuckerman
Yale University
Time
and Location: November 15 2 pm in MS 6627
Title:
Harmonic Algebra
Abstract:
Traditional harmonic analysis deals with representations of groups by
linear operators on function spaces. By harmonic algebra, we refer to
representations of Lie groups, Lie algebras, or Hopf algebras (such
as quantum groups) by, respectively, automorphisms, derivations, or
Hopf actions on associative algebras (possibly noncommutative). A typical
example arises by considering a left and right translation invariant
subalgebra of the ring of smooth functions on a Lie group. A more contemporary
example arises from the noncommutative coordinate ring of a quantum
group. The Harish-Chandra Schwartz space of a semisimple Lie group is
especially well suited to our theory of harmonic algebra. The ring of
smooth functions on a Lie group modulo a cocompact discrete subgroup
provides another excellent example. The theory of cohomological induction,
as developed by Knapp, Vogan and the speaker, is especially transparent
under the spotlight of harmonic algebra.
Background on Professor Zuckerman:
Gregg
Zuckerman has made fundamental contributions to the representation
theory of semisimple Lie groups. The Zuckerman functors which he invented
have played a basic role in representation theory of these groups. His
work, by himself and with David Vogan, is basic to theory of automorphic
forms and Shimura varieties. More recently, he has been deeply interested
in representation theoretic aspects of string theory, topological field
theories, and infinite dimensional Lie groups and Lie algebras. He has
been teaching at Yale since 1975. |
