Automorphisms of unipotent subgroups of lie type groups of small ranks

Levchuk, V. M.

doi:10.1007/bf02001355

Cited by 14 publications

(11 citation statements)

References 3 publications

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“…If we substitute the expression for $3 (n) from (28) into (13) then after a straightforward computation we get the assertion in theorem 1.…”

Section: Fr P(x)mentioning

confidence: 96%

“…By [13], we may consider the group UO(K) as the adjoint group of the algebra NO(K). Further, for roots r,s E O, we suppose s < r, if r -s is linear combination of fundamental roots with non-negative coefficients.…”

Section: Construction and Enumeration Of Idealsmentioning

confidence: 99%

“…(2) [13], if auv were renamed through au-l,v. The number of all the It is obtained from Bn+ 1 steplines from aiv to akin (v < m < k < n, Iv] < i < k) is denoted by N [(i,v); (k,m)].…”

Section: Rm)+ ~ Kermentioning

confidence: 99%

“…(1) Further, let's use representation of the algebra NO(K) of classic-type by O+-matfices, pointed out in [13]. As well as root notation .°° a n , -n ... a n , -1 ano anl ... ann…”

Section: Rm)+ ~ Kermentioning

confidence: 99%

“…The unipotent subgroup U~(K) of the Chevalley group of the type • over K is treated in [13] as the adjoint group of the algebra NO(K). Denote by c(~, K), the number of all characteristic subgroups of the group U~(K), and by d(~, K), the number of all D-invariant normal subgroups of U~(K).…”

Section: Introductionmentioning

confidence: 99%

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Enumeration in the Chevalley algebras

Егорычев¹,

Levchuk²

2001

SIGSAM Bull.

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l e v c h u k @ l a n , k r a s u , r u i e v c h u k @ h o m e , k r a s n o y a r s k , r u AbstractWe consider the maximal nilpotent subalgebra N~(K) of the Chevalley algebra of the type over an arbitrary field K. Our purpose is enumeration of ideals of NO(K) that are invariant under the subgroup D of all diagonal automorphisms. Connections between ideals of NO(K) and normal subgroups of the unipotent subgroup of the Chevalley group of the type • over K are used. Finally, we use methods of integral representation of sums and of listing lattice paths. We also discuss some other problems of the enumeration of ideals.

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“…If we substitute the expression for $3 (n) from (28) into (13) then after a straightforward computation we get the assertion in theorem 1.…”

Section: Fr P(x)mentioning

confidence: 96%

Section: Construction and Enumeration Of Idealsmentioning

confidence: 99%

“…(2) [13], if auv were renamed through au-l,v. The number of all the It is obtained from Bn+ 1 steplines from aiv to akin (v < m < k < n, Iv] < i < k) is denoted by N [(i,v); (k,m)].…”

Section: Rm)+ ~ Kermentioning

confidence: 99%

“…(1) Further, let's use representation of the algebra NO(K) of classic-type by O+-matfices, pointed out in [13]. As well as root notation .°° a n , -n ... a n , -1 ano anl ... ann…”

Section: Rm)+ ~ Kermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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