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Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic

Research output: Thesis › Doctoral Thesis

Unpublished

Standard

Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic. / Johnson, Heather.
Lancaster University, 2015. 148 p.

Research output: Thesis › Doctoral Thesis

Harvard

Johnson, H 2015, 'Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic', PhD, Lancaster University.

APA

Johnson, H. (2015). Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic. [Doctoral Thesis, Lancaster University]. Lancaster University.

Vancouver

Johnson H. Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic. Lancaster University, 2015. 148 p.

Author

Johnson, Heather. / Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic. Lancaster University, 2015. 148 p.

Bibtex

@phdthesis{3e202ce7e4944f6eab31180072f9b205,
title = "Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic",
abstract = "Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component.",
author = "Heather Johnson",
year = "2015",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - BOOK

T1 - Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic

AU - Johnson, Heather

PY - 2015

Y1 - 2015

N2 - Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component.

AB - Let N1 denote the restricted nullcone of the Lie algebra g of a simple algebraic group in characteristic p>0, i.e. the set of x∈g such that x|p| = 0. For representatives e1,...,en of the nilpotent orbits of g we find the irreducible components of gei∩N1 for g = G2 and F4 in good characteristic p. We do the same for g = E6 with the exception of three nilpotent orbits. We use this information to determine the irreducible components of the restricted nilpotent commuting variety C1nil(g)= {(x,y) ∈ N1×N1 : [x,y] = 0} for g = G2 and F4. We do the same for g = E6 with the exception of when p=7 where we describe C1nil(g) as the union of an irreducible set of dimension 78 and one of dimension 76 which may or may not be an irreducible component.

M3 - Doctoral Thesis

PB - Lancaster University

ER -