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Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists a number $C$ such that the multiplicity $\dim Hom(\rho,\mathbb{C}[X(F)])$… Click to show full abstract
Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists a number $C$ such that the multiplicity $\dim Hom(\rho,\mathbb{C}[X(F)])$ is bounded by $C$, for any finite field $F$ and any irreducible representation $\rho$ of $G(F)$. We give an explicit bound for $C$. We conjecture that this result is true for any reductive group scheme and when $F$ ranges (in addition) over all local fields of characteristic $0$.
Keywords:
spaces finite;
bounds multiplicities;
scheme;
multiplicities spherical;
spherical spaces;
finite fields
Journal Title: Journal of Pure and Applied Algebra
Year Published: 2019
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Journal Title: Journal of Pure and Applied Algebra
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!