Support varieties for Weyl modules over bad primes

David John Benson; Brian D. Boe; Leonard Chastkofsky; Daniel K. Nakano; Jo Jang Hyun; Jonathan Kujawa; Nadia Mazza; Philip Bergonio; Bobbe Cooper; Jeremiah Hower; Kenyon J. Platt; Caroline Wright; UGA VIGRE Algebra Group

doi:10.1016/j.jalgebra.2007.03.008

Support varieties for Weyl modules over bad primes

David John Benson, Brian D. Boe, Leonard Chastkofsky, Daniel K. Nakano, Jo Jang Hyun, Jonathan Kujawa, Nadia Mazza, Philip Bergonio, Bobbe Cooper, Jeremiah Hower, Kenyon J. Platt, Caroline Wright, UGA VIGRE Algebra Group

Mathematical Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let G be a reductive algebraic group scheme defined over F-p and G(1) be the first Frobenius kernel. For any dominant weight lambda, one can construct the Weyl module V(lambda). When p is a good prime for G, the G(1)-support variety of V (lambda) was computed by Nakano, Parshall and Vella in [D. K. Nakano, B.J. Parshall, D.C. Vella, Support varieties for algebraic groups, J. Reine Angew. Math. 547 (2002) 15-49]. We complete this calculation by computing the G(1)-supports of the Weyl modules over fields of bad characteristic.

Original language	English
Pages (from-to)	602-633
Number of pages	32
Journal	Journal of Algebra
Volume	312
Issue number	2
Early online date	21 Mar 2007
DOIs	https://doi.org/10.1016/j.jalgebra.2007.03.008
Publication status	Published - 15 Jun 2007

Keywords

cohomology
support varieties
Weyl modules
finite-group schemes
lie-algebras
nilpotent elements
unipotent elements
field

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10.1016/j.jalgebra.2007.03.008

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Support varieties for Weyl modules over bad primes. / Benson, David John; Boe, Brian D.; Chastkofsky, Leonard; Nakano, Daniel K.; Jang Hyun, Jo; Kujawa, Jonathan; Mazza, Nadia; Bergonio, Philip; Cooper, Bobbe; Hower, Jeremiah; Platt, Kenyon J.; Wright, Caroline; UGA VIGRE Algebra Group.

In: Journal of Algebra, Vol. 312, No. 2, 15.06.2007, p. 602-633.

Research output: Contribution to journal › Article › peer-review

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abstract = "Let G be a reductive algebraic group scheme defined over F-p and G(1) be the first Frobenius kernel. For any dominant weight lambda, one can construct the Weyl module V(lambda). When p is a good prime for G, the G(1)-support variety of V (lambda) was computed by Nakano, Parshall and Vella in [D. K. Nakano, B.J. Parshall, D.C. Vella, Support varieties for algebraic groups, J. Reine Angew. Math. 547 (2002) 15-49]. We complete this calculation by computing the G(1)-supports of the Weyl modules over fields of bad characteristic.",

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AU - Benson, David John

AU - Boe, Brian D.

AU - Chastkofsky, Leonard

AU - Nakano, Daniel K.

AU - Jang Hyun, Jo

AU - Kujawa, Jonathan

AU - Mazza, Nadia

AU - Bergonio, Philip

AU - Cooper, Bobbe

AU - Hower, Jeremiah

AU - Platt, Kenyon J.

AU - Wright, Caroline

AU - UGA VIGRE Algebra Group

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AB - Let G be a reductive algebraic group scheme defined over F-p and G(1) be the first Frobenius kernel. For any dominant weight lambda, one can construct the Weyl module V(lambda). When p is a good prime for G, the G(1)-support variety of V (lambda) was computed by Nakano, Parshall and Vella in [D. K. Nakano, B.J. Parshall, D.C. Vella, Support varieties for algebraic groups, J. Reine Angew. Math. 547 (2002) 15-49]. We complete this calculation by computing the G(1)-supports of the Weyl modules over fields of bad characteristic.

KW - cohomology

KW - support varieties

KW - Weyl modules

KW - finite-group schemes

KW - lie-algebras

KW - nilpotent elements

KW - unipotent elements

KW - field

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JF - Journal of Algebra

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Support varieties for Weyl modules over bad primes

Abstract

Keywords

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