Bilinear and Quadratic Forms on Rational Modules of Split Reductive Groups. (1st April 2016)

• Record Type: Journal Article
• Authors: Garibaldi, Skip; Nakano, Daniel K.
• Is Part Of: Canadian journal of mathematics. Volume 68:Number 2(2016)
• Page Start: 395
• Page End: 421
• Publication Date: 2016-04-01
• Subjects: 20G05 -- 11E39 -- 11E88 -- 15A63 -- 20G15; orthogonal representations -- symmetric tensors -- alternating forms -- characteristic 2 -- split reductive groups; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2015-042-5
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the questions of whether a given complex representation is symplectic or orthogonal have been solved since at least the 1950s. Similar results for Weyl modules of split reductive groups over fields of characteristic different from 2 hold by using similar proofs. This paper considers analogues of these results for simple, induced, and tilting modules of split reductive groups over fields of prime characteristic as well as a complete answer for Weyl modules over fields of characteristic 2.