ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 22C05 Carina Boyallian, Massachusetts Institute of Technology, USA; Universidad Nacional de Córdoba, Argentina Argentina On Bernstein polynomials for compact Lie groups Let A(G) be the ring of representative functions on a compact connected Lie group G. By the theory of D-modules, given f ∈ A(G), we have the following functional equation D(g, s)(f(g))^{s+1} = b(s)(f(g))^{s} where D(g, s) belongs to the ring of differential operators D(G)[s] and b(s) ∈ ℂ[s]. The monic polynomial of minimal degree which satisfies this equation is called the Bernstein polynomial attached to f. We give the Bernstein Polynomials for basic matrix entries of irreducible unitary representations of compact Lie group SU(2), an application to the analytic continuation of certain distributions on SU(2) and we describe the Bernstein polynomial for B_{−} × B-semi-invariant functions on a semisimple complex Lie group. Reference: Carina Boyallian, On Bernstein polynomials for compact Lie groups. Partially accepted in Journal of Algebra.