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

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

Access to Document

10.1016/j.jalgebra.2007.03.008

Cite this

Benson, D. J., Boe, B. D., Chastkofsky, L., Nakano, D. K., Jang Hyun, J., Kujawa, J., Mazza, N., Bergonio, P., Cooper, B., Hower, J., Platt, K. J., Wright, C., & UGA VIGRE Algebra Group (2007). Support varieties for Weyl modules over bad primes. Journal of Algebra, 312(2), 602-633. https://doi.org/10.1016/j.jalgebra.2007.03.008

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

@article{e6e2f953e8f146909525be08ee19c5f1,

title = "Support varieties for Weyl modules over bad primes",

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.",

keywords = "cohomology, support varieties, Weyl modules, finite-group schemes, lie-algebras, nilpotent elements, unipotent elements, field",

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

year = "2007",

month = jun,

day = "15",

doi = "10.1016/j.jalgebra.2007.03.008",

language = "English",

volume = "312",

pages = "602--633",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Support varieties for Weyl modules over bad primes

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

PY - 2007/6/15

Y1 - 2007/6/15

N2 - 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.

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

U2 - 10.1016/j.jalgebra.2007.03.008

DO - 10.1016/j.jalgebra.2007.03.008

M3 - Article

VL - 312

SP - 602

EP - 633

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -