Project Details
Projekt
Asymptotic branching laws for finite dimensional representations of complex reductive Lie groups by geometric methods
Applicant
Dr. Henrik Seppänen
Subject Area
Mathematics
Term
from 2012 to 2015
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 219517417
A fundamental problem in representation theory is that of decomposing an irreducible representation Π of a group G into irreducible representations of a subgroup, L, of G. For a finite dimensional representation Π of a complex reductive Lie group G the solution of this problem is given in principle by Kostant’s branching theorem, which gives a combinatorial expression for the multiplicities of the irreducible L-representations. However, the formula for the multiplicities is given by an alternating sum where cancellation occurs. It is desirable to have formulas for multiplicities given by a priori positive terms, such as for instance by counting the number of integral points of some convex polytope, or compact convex set, of Rn. We propose to construct convex bodies Δ in Rn, such that the integral points of Δ count multiplicities, at least in an asymptotic sense, of irreducible L- representations of Π. The bodies are to be constructed by the geometric realization of the representation Π as the space of holomorphic sections of a line bundle over a flag variety X. The idea is that Δ should encode the behaviour of holomorphic sections along a complete flag X(0)<...
DFG Programme
Priority Programmes
Subproject of
SPP 1388:
Representation Theory
