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Glasby, John S.

doi:10.1007/978-1-4615-8807-8_16

Cited by 2 publications

(4 citation statements)

References 45 publications

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“…Computation played a key role in establishing this theorem. The Magma code available at [3] was useful for both conjecturing the truth of Theorem 2.5, and for discovering the key identity of Lemma 7.5 from which we constructed our proof. First we show that G(r, p) has a generating set of size less than rp.…”

Section: The Groups G(r P)mentioning

confidence: 99%

“…Indeed we prove in Theorem 2.5 that G(r, p) = S a ≀ D b is a wreath product of a the symmetric group of degree a, and the dihedral group of degree b. We discovered the essential idea for the proof by using a Magma computer programs available at [3]. This computational insight allowed us to replace a number of difficult partial results with a relatively short proof of Theorem 2.5.…”

Section: Introductionmentioning

confidence: 99%

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‘Norman involutions’ and tensor products of unipotent Jordan blocks

2019

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This paper studies the Jordan canonical form (JCF) of the tensor product of two unipotent Jordan blocks over a field of prime characteristic p. The JCF is characterized by a partition λ = λ(r, s, p) depending on the dimensions r, s of the Jordan blocks, and on p. Equivalently, we study a permutation π = π(r, s, p) of {1, 2, . . . , r} introduced by Norman. We show that π(r, s, p) is an involution involving reversals, or is the identity permutation. We prove that the group G(r, p) generated by π(r, s, p) for all s, "factors" as a wreath product corresponding to the factorisation r = ab as a product of its p ′ -part a and p-part b: precisely G(r, p) = S a ≀ D b where S a is a symmetric group of degree a, and D b is a dihedral group of degree b. We also give simple necessary and sufficient conditions for π(r, s, p) to be trivial.

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Section: The Groups G(r P)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

‘Norman involutions’ and tensor products of unipotent Jordan blocks

2019

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“…To prove Theorem 3.1 we need a technical lemma which we have not been able to find in the literature, see [4]. Lemma 3.2 below says i 1 λ i = i 1 λ ′ i when k = 1.…”

Section: Conjugate Partitionsmentioning

confidence: 99%

“…Further by Theorem 2.9 dim(C(N λ , N µ )) = i 1 λ ′ i µ ′ i where, as usual, λ ′ and µ ′ denote conjugate partitions. We use the observation: (4) if 0 x a and 0 y b, then (a − x)(b − y) + xy ab to show that dim (C(A, B)…”

Section: Upper and Lower Bounds For Dim Fmentioning

confidence: 99%

On the parameters of intertwining codes

Glasby

Praeger²

2018

Ars Math. Contemp.

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Let F be a field and let F r×s denote the space of r×s matrices over F . Given, then for each i ∈ I, the characteristic polynomials of A i and B i and share a nontrivial factor. We give an exact formula for k = dim (C(A, B)) and give upper and lower bounds. This generalizes previous work. Finally we construct intertwining codes with large minimum distance when the field is not 'too small'. We give examples of codes where d = rs/k = 1/R is large where the minimum distance, dimension, and rate of the linear code C(A, B) are denoted by d, k, and R = k/rs, respectively.

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Cited by 2 publications

References 45 publications

‘Norman involutions’ and tensor products of unipotent Jordan blocks

‘Norman involutions’ and tensor products of unipotent Jordan blocks

On the parameters of intertwining codes

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