Complex representations of the full linear group over a finite field

Faddeev, D. K.

doi:10.1007/bf01085053

Cited by 8 publications

(16 citation statements)

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“…With K a field of characteristic different from that of F, this was Proposition 5 in Faddeev's paper [3]. While that proposition was introduced with the words "From all that has been said there follows", the sentence before that said that "The full proof [of the previous proposition] "is complicated, and we omit it", and that proof has remained unpublished.…”

Section: The Resultsmentioning

confidence: 99%

“…While that proposition was introduced with the words "From all that has been said there follows", the sentence before that said that "The full proof [of the previous proposition] "is complicated, and we omit it", and that proof has remained unpublished. The "route to the proof described in [3] relied on details from the representation theory of finite general linear groups. The aim of this paper is to present a complete and self-contained proof of the result, in the generality stated above.…”

Section: The Resultsmentioning

confidence: 99%

“…These observations have reduced the lemma to the claim that dorn n does have complements U satisfying (3) and that when F is finite the number of such complements is a power of the characteristic of F .…”

Section: Proof Of Lemma 4 Dimension Count Shows That If P Is One Of mentioning

confidence: 99%

“…We have proved that if one takes (5) as a definition, chooses U¡c_l, ... , Ux in that order subject only to (6), and finally chooses U subject to (7), then the U so obtained is a complement to dom7r that satisfies (3) and that each such complement is canonically obtained this way. When F is finite, the number of complements of a subspace in an F-space is always a power of the number of elements of F , so the total number of choices in this canonical construction is a power of the characteristic of F .…”

Section: Proof Of Lemma 4 Dimension Count Shows That If P Is One Of mentioning

confidence: 99%

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Semigroup algebras of the full matrix semigroup over a finite field

Kovács¹

1992

Proc. Amer. Math. Soc.

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Abstract.Let M denote the multiplicative semigroup of all n-by-n matrices over a finite field F and K a commutative ring with an identity element in which the characteristic of F is a unit. It is proved here that the semigroup algebra K[M] is the direct sum of n + 1 algebras, namely, of one full matrix algebra over each of the group algebras K[GL(r, F)] with r = 0, 1, ... , ». The degree of the relevant matrix algebra over A" [GL(r, F)] is the number of /■-dimensional subspaces in an «-dimensional vector space over F .For K a field of characteristic different from that of F , this result was announced by Faddeev in 1976. He only published an incomplete sketch of his proof, which relied on details from the representation theory of finite general linear groups. The present proof is self-contained.

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Section: The Resultsmentioning

confidence: 99%

Section: The Resultsmentioning

confidence: 99%

Section: Proof Of Lemma 4 Dimension Count Shows That If P Is One Of mentioning

confidence: 99%

Section: Proof Of Lemma 4 Dimension Count Shows That If P Is One Of mentioning

confidence: 99%

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Semigroup algebras of the full matrix semigroup over a finite field

Kovács¹

1992

Proc. Amer. Math. Soc.

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“…Then Y = eX is a disjoint union of (/-orbits r,, ... , Y t . Let [3] Embedding finite semigroup amalgams 491…”

Section: Resultsmentioning

confidence: 99%

Embedding finite semigroup amalgams

Okniński

Putcha

1991

J Aust Math Soc A

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Let S, 7"[, ... , T k be finite semigroups and p,: S •-• T t be embeddings. When CIS] is semisimple, we find necessary and sufficient conditions for the semigroup amalgam (T x , ... , T k ; S) to be embeddable in a finite semigroup. As a consequence we show that if S is a finite semigroup with C[S] semisimple, then S is an amalgamation base for the class of finite semigroups if and only if the principal ideals of 5 are linearly ordered. Our proof uses both the theory of representations by transformations and the theory of matrix representations as developed by Clifford, Munn and Ponizovskii

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Complex representations of classical groups over a finite field

Nagornyi¹

1981

J Math Sci

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Complex representations of the full linear group over a finite field

Cited by 8 publications

References 5 publications

Semigroup algebras of the full matrix semigroup over a finite field

Semigroup algebras of the full matrix semigroup over a finite field

Embedding finite semigroup amalgams

Complex representations of classical groups over a finite field

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