Peter-Weyl Theorem and Representation of SU(2)

Mandal, Rahul (2021) Peter-Weyl Theorem and Representation of SU(2). Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Rahul Mandal (Roll No. 16MS065)) 16MS065_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (326kB)

Abstract

In this article we prove that a complex Hilbert space H can be splitted into an orthogonal direct sum of irreducible finite dimensional unitary representations of G.Then we prove the Peter-Weyl’s Theorem by showing the space of the square integrable functions on G can be decomposed into orthogonal direct sum of the irreducible unitary representations.Next we discuss how the Fourier series is developed for the non-commutative compact Lie groups SU(2).Here, we use the theory of characters and the calculation of the Haar measure,then the representation constructed in the section 11 will be shown as the equivalence of any irreducible unitary representations for SU(2).At the end ,we will discuss the Fourier series of smooth functions on SU(2).

Actions (login required)

View Item