Weil representations of unitary groups over ramified extensions of finite local rings with odd nilpotency length. Issue 8 (3rd August 2019)

• Record Type: Journal Article
• Authors: Szechtman, Fernando; Shau, Momuita; Herman, Allen
• Is Part Of: Communications in algebra. Volume 47:Issue 8(2019)
• Page Start: 3007
• Page End: 3024
• Publication Date: 2019-08-03
• Subjects: local rings -- unitary groups -- Weil representations; Primary: 20G05 Secondary: 20C15 -- 11E39 -- 11E57; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1549663
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: We find the irreducible decomposition of the Weil representation of the unitary group U 2 n ( A ), where A is a ramified quadratic extension of a finite, commutative, local, principal ideal ring R and the nilpotency degree of the maximal ideal of A is odd. We show in particular that this Weil representation is multiplicity free. Restriction to the special unitary group SU 2 n ( A ) preserves irreducibility and multiplicity freeness provided n > 1.