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

Dilchand Mahto; Jagmohan Tanti

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

Volume 17, Issue 3 Pages 29-44 December 30, 2021 381 downloads

Article overview

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 formsRepresentation theoryVector spaceDirect sums.

AMS Subject Classification

20C33, 15A63, 15A03.

Reference information

How to Cite

Dilchand Mahto, Jagmohan Tanti (2021). SPACE OF INVARIANT BILINEAR FORMS UNDER A REPRESENTATION OF $SL_2(3)$. South East Asian Journal of Mathematics and Mathematical Sciences, 17(3), 29-44.

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