Work

Projections Separating Spectra for $\boldsymbol{L^2}$ on Pseudounitary Groups $\boldsymbol{{\mathrm U}(p,q)}$

Year: 2017

Type: article

Abstract: The spectrum of |$L^2$| on a pseudo-unitary group |${\mathrm U}(p,q)$| (we assume |$p\geqslant q$|⁠) naturally splits into |$q+1$| types. We give explicit formulas for the orthogonal projections in |$L^2$| to subspaces with uniform spectra (this is an old question formulated by Gelfand and Gindikin). We also write two finer separations of |$L^2$|⁠. In the first case, pieces are parametrized by |$r=0, 1, \ldots, q$| and representations of the discrete series of |${\mathrm U}(p-r,q-r)$|⁠, where |$r=0, \ldots, q$|⁠. In the second case, pieces are parametrized by all discrete parameters of the tempered spectrum of |${\mathrm U}(p,q)$|⁠.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnx268

Author: Yury A Neretin

Institutions: University of Vienna, Lomonosov Moscow State University, Institute for Information Transmission Problems, Institute for Theoretical and Experimental Physics

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Austrian Science Fund

Award: G3803984520