Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Gutiérrez Frez, L., Pantoja, J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147110
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution / L. Gutiérrez Frez, J. Pantoja // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ.

We construct a complex linear Weil representation ρ of the generalized special linear group G=SL¹∗(2,An) (An=K[x]/⟨xⁿ⟩, K the quadratic extension of the finite field k of q elements, q odd), where An is endowed with a second class involution. After the construction of a specific data, the representa...