### 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 dimHom(ρ,C[X(F)]) is bounded by C, for any finite field F and any irreducible representation ρ 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. Different aspects of this conjecture were studied in [3,11,6,7].

Original language | English (US) |
---|---|

Pages (from-to) | 3859-3868 |

Number of pages | 10 |

Journal | Journal of Pure and Applied Algebra |

Volume | 223 |

Issue number | 9 |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

### Fingerprint

### Keywords

- Representations of groups of Lie type

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Pure and Applied Algebra*,

*223*(9), 3859-3868. https://doi.org/10.1016/j.jpaa.2018.12.008

}

*Journal of Pure and Applied Algebra*, vol. 223, no. 9, pp. 3859-3868. https://doi.org/10.1016/j.jpaa.2018.12.008

**Bounds on multiplicities of spherical spaces over finite fields.** / Aizenbud, Avraham; Avni, Nir.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bounds on multiplicities of spherical spaces over finite fields

AU - Aizenbud, Avraham

AU - Avni, Nir

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 dimHom(ρ,C[X(F)]) is bounded by C, for any finite field F and any irreducible representation ρ 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. Different aspects of this conjecture were studied in [3,11,6,7].

AB - 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 dimHom(ρ,C[X(F)]) is bounded by C, for any finite field F and any irreducible representation ρ 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. Different aspects of this conjecture were studied in [3,11,6,7].

KW - Representations of groups of Lie type

UR - http://www.scopus.com/inward/record.url?scp=85059625359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059625359&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2018.12.008

DO - 10.1016/j.jpaa.2018.12.008

M3 - Article

VL - 223

SP - 3859

EP - 3868

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 9

ER -