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Research output: Thesis › Doctoral Thesis

Unpublished

Lancaster University, 2015. 148 p.

Research output: Thesis › Doctoral Thesis

Johnson, H 2015, 'Irreducible components of the restricted nilpotent commuting variety of G_{2}, F_{4} and E_{6} in good characteristic', PhD, Lancaster University.

Johnson, H. (2015). *Irreducible components of the restricted nilpotent commuting variety of G*_{2}, F_{4} and E_{6} in good characteristic. [Doctoral Thesis, Lancaster University]. Lancaster University.

Johnson H. Irreducible components of the restricted nilpotent commuting variety of G_{2}, F_{4} and E_{6} in good characteristic. Lancaster University, 2015. 148 p.

@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",

}

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 -