Irreducible characters of 
                $$\mathrm{GSp}(4, q)$$
                      GSp
                      (
                      4
                      ,
                      q
                      )
               and dimensions of spaces of fixed vectors

Breeding, Jeffery

doi:10.1007/s11139-014-9622-3

Ramanujan J

2014

DOI: 10.1007/s11139-014-9622-3

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Irreducible characters of $$\mathrm{GSp}(4, q)$$ GSp ( 4 , q ) and dimensions of spaces of fixed vectors

Jeffery Breeding

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Cited by 6 publications

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Parahoric Restriction for GSp(4)

Rösner

2017

Algebr Represent Theor

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Parahoric restriction is the parahoric analogue of Jacquet's functor. Fix an arbitrary parahoric subgroup of the group GSp(4, F ) of symplectic similitudes of genus two over a local number field F/Q p . We determine the parahoric restriction of the non-cuspidal irreducible smooth representations in terms of explicit character values. IntroductionFor a reductive connected group G over a local number field F/Q p , with group of Fvalued points G = G(F ), fix a compact parahoric subgroup P ⊆ G with pro-unipotent radical P + . The parahoric restriction functor between categories of admissible representationsis the parahoric analogue of Jacquet's functor of parabolic restriction. It assigns to an admissible representation (ρ, V ) of G the action of the Levi quotient P/P + on the space of invariants under P + . The functor is exact and factors over semisimplification, so it is sufficient to study irreducible admissible representations.For the group G = GSp(4) of symplectic similitudes of genus two, we determine the parahoric restriction of non-cuspidal irreducible admissible representations in terms of explicit character values for the finite Levi quotient P/P + . This has applications in the theory of Siegel modular forms of genus two, invariant under principal congruence subgroups of squarefree level. Main resultFor a proper parabolic subgroup of G = GSp(4, F ) fix a cuspidal irreducible admissible complex linear representation σ of its Levi quotient. Let ρ be a subquotient of the normalized parabolic induction of σ to G. Then ρ is non-cuspidal and every non-cuspidal irreducible admissible representation of G arises this way.

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Parahoric Restriction for GSp(4)

Rösner

2017

Algebr Represent Theor

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Groups with few p′-character degrees

Giannelli

Rizo

Fry

2020

Journal of Pure and Applied Algebra

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The Gelfand-Graev Representation of GSp(4, 𝔽_q)

Breeding-Allison

Rainbolt

2016

Communications in Algebra

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Irreducible characters of $$\mathrm{GSp}(4, q)$$ GSp ( 4 , q ) and dimensions of spaces of fixed vectors

Cited by 6 publications

References 9 publications

Parahoric Restriction for GSp(4)

Parahoric Restriction for GSp(4)

Groups with few p′-character degrees

The Gelfand-Graev Representation of GSp(4, 𝔽_q)

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Irreducible characters of $$\mathrm{GSp}(4, q)$$ GSp ( 4 , q ) and dimensions of spaces of fixed vectors

Cited by 6 publications

References 9 publications

Parahoric Restriction for GSp(4)

Parahoric Restriction for GSp(4)

Groups with few p′-character degrees

The Gelfand-Graev Representation of GSp(4, 𝔽q)

Contact Info

Product

Resources

About

The Gelfand-Graev Representation of GSp(4, 𝔽_q)