Geometric Weil representations for star-analogues of SL(2,k)

2010/06/27 by Luis Gutiérrez-Frez, Gutiérrez-Frez, Luis, José Pantoja +3
Mathematics · #15A33 #16W10 #17B37 #20F05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary 20C33 #Representation Theory (math.RT) #Secondary 20C25 #math.RT #msc:15A33 #msc:16W10 #msc:17B37 #msc:20C25 #msc:20C33 #msc:20F05

paper · pdf · doi:10.48550/arxiv.1006.5236

15 pages, submitted to Proceedings of the XVIII Latin American Algebra Colloquium (CLA XVIII)

arxiv created 2010/06/27 · openalex publication_date 2010/06/27 · arxiv updated 2010/06/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present here an elementary geometric approach to the construction of Weil representations of the star-analogues SL_∗(2,A), A a ring or algebra with involution ∗, of the group SL(2, k), k a field, reminiscent of the quantum groups SL_q(2,A). We review as well the elementary construction of Weil representations for these groups via generators and relations, which uses the Bruhat presentation available in many cases. We compare the representations obtained by both methods in the non - classical case of the finite truncated polynomial algebra A_m of degree m with its canonical involution and obtain the analogue of the Maslov Index in this case.

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