منابع مشابه
Primitive central idempotents of finite group rings of symmetric groups
Let p be a prime. We denote by Sn the symmetric group of degree n, by An the alternating group of degree n and by Fp the field with p elements. An important concept of modular representation theory of a finite group G is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring FqG, where q is a prime...
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In this paper, we prove the following two theorems. Theorem 1 Let 0 denote a distance-regular graph with diameter d ≥ 3. Suppose E and F are primitive idempotents of 0, with cosine sequences σ0, σ1, . . . , σd and ρ0, ρ1, . . . , ρd , respectively. Then the following are equivalent. (i) The entry-wise product E ◦ F is a scalar multiple of a primitive idempotent of 0. (ii) There exists a real nu...
متن کاملPrimitive central idempotents of finite group rings of symmetric and alternating groups in characteristic 2
and call it the essential weight of the partition μ. For our purpose it is convenient to ignore the parts equal to 1 in the partition because an element like (1, 2, 3) ∈ S3 is also an element of bigger symmetric groups. So we write μ = 22 , ..., nn for a partition and the corresponding class Cμ is a class of an arbitrary symmetric group Sn with n ≥ W (μ) depending on the context, i.e. C2 denote...
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We exhibit the primitive central idempotents of a semisimple group algebra of a finite nilpotent group over an arbitrary field (without using group characters), examining the abelian case separately. Our result extends and improves the main result in [1].
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We construct a recursive formula for a complete system of primitive orthogonal idempotents for any Rtrivial monoid. This uses the newly proved equivalence between the notions of R-trivial monoid and weakly ordered monoid. Résumé. Nous construisons une formule récursive pour un système complet d’idempotents orthogonaux primitifs pour tout monoı̈de R-trivial. Nous employons une nouvelle équivalenc...
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ژورنال
عنوان ژورنال: Mathematica Moravica
سال: 2001
ISSN: 1450-5932,2560-5542
DOI: 10.5937/matmor0105007b