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Research output: Thesis › Doctoral Thesis
Research output: Thesis › Doctoral Thesis
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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 -