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

Johnson, Heather (2015) Irreducible components of the restricted nilpotent commuting variety of G2, F4 and E6 in good characteristic. PhD thesis, UNSPECIFIED.

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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.

Item Type:
Thesis (PhD)
ID Code:
76230
Deposited By:
Deposited On:
21 Oct 2015 05:11
Refereed?:
No
Published?:
Unpublished
Last Modified:
24 Nov 2020 09:05