ℙ\mathfrakgl₂ is Multiplicity-Free as a PGL₂ × PGL₂-Variety

2019/12/10 by Dmitry Gourevitch, Shai Keidar, Gourevitch, Dmitry +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #math.AG #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1912.04997

MSc thesis completed at Weizmann Institute of Science under the guidance of Prof. Dmitry Gourevitch

arxiv created 2019/12/10 · openalex publication_date 2019/12/10 · arxiv updated 2019/12/12 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

Let F be a non-Archimedean local field. Let G be an algebraic group over F. A G-variety X defined over F is said to be multiplicity-free if for any admissible irreducible representation π of G(F) the following takes place: dim Hom_G(F)(S(X(F)), π) ≤ 1 where S(X(F)) is the space of Schwartz functions on X(F). In this thesis we prove that ℙ\mathfrakgl₂(F) is multiplicity-free as a PGL₂(F)× PGL₂(F)-variety.

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