Star-product formulas on finite groups

  • Francis Deocareza Delloro Department of Mathematics, Ateneo de Naga University
  • Job Agcaoili Nable Department of Mathematics, Ateneo de Manila University

Abstract

Given a finite group G, associative and noncommutative products * will be constructed on the function space L²(G), where these star-products are parametrized by the unitary dual  of G. If Rf:L²(G)→ L²(G) is the convolution operator Rf(f1)=f*f1, then the projections of Rf on the irreducible spaces of the elements of is equivalent to Rf*, Rf*(f1)=f*f1. It is thus natural to consider Harmonic Analysis/Quantum Mechanics on L²(G) using the star-product. In this work, we establish star-product formulas on finite groups, both in the position and momentum representation.

Published
2019-05-13
How to Cite
[1]
F. Delloro and J. Nable. Star-product formulas on finite groups, Proceedings of the Samahang Pisika ng Pilipinas 37, SPP-2019-2D-04 (2019). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2019-2D-04.
Section
Theoretical and Mathematical Physics