SPACE OF INVARIANT BILINEAR FORMS UNDER A REPRESENTATION OF $SL_2(3)$

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 262

Volume : 17 , Issue : 3
DOI:
Author :
Dilchand Mahto (Department of Mathematics, Central University of Jharkhand, Ranchi - 835205, Jharkhand, INDIA)
Jagmohan Tanti (Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow - 226025, Uttar Pradesh, INDIA)

Abstract

Let $n$ be a positive integer. In this paper we compute the space of invariant bilinear forms under an $n$ degree representation of the special linear group $SL_2(3)$ and its dimension over the complex field $\mathbb{C}$. We discuss the existence of a non-degenerate invariant bilinear form explicitly.

Keywords and Phrases

Bilinear forms, Representation theory, Vector space, Direct sums.

A.M.S. subject classification

20C33, 15A63, 15A03.

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