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Specht Modules of Trivial Source and the Endomorphism Ring of the Lie Module
Başlık:
Specht Modules of Trivial Source and the Endomorphism Ring of the Lie Module
Yazar:
Hudson, Tara Alexandra, author.
ISBN:
9780438049086
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (83 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: David Hemmer Committee members: Bernard Badzioch; Yiqiang Li.
Özet:
Part I: Specht Modules of Trivial Source. The source of a Specht module is not generally known, unless it is a projective or irreducible module and in this case the source is trivial. Are these the only Specht modules with trivial source? To address this question, we classify the Specht modules of FSigma2p and FSigma2p+1 with trivial source for p ≥ 3. It turns out that a Specht module of FSigma2p and FSigma2p +1 corresponding to a weight two partition has trivial source if and only if it is irreducible. On the other hand, there are Specht modules corresponding to weight one partitions that are not irreducible but have trivial source, these can be identified by ordering the partitions (using the lexicographic ordering) in the block to which they belong. The result concerning Specht modules corresponding to weight one partitions with trivial source is not unique to FSigma2p and FSigma2p +1, but it generalizes to Specht modules of FSigman for any 5 ≤ p ≤ n.
Part II: On the Endomorphism Ring of the Lie Module. Let F be a field of nonzero characteristic which contains a primitive rth root of unity, and let fj be a particular Lie idempotent. In this paper, we analyze fj FSigmar fj, in hopes of answering a conjecture posed by Doty and Douglass in [7]. It is known that fj FSigma r fj ≅ EndF Sigmar(FSigma r fj), and for (r, j)=1 this indicates that fj FSigma r fj ≅ EndF Sigmar(Lie(r)), where Lie(r) denotes the Lie module. We construct a basis for EndF Sigmar(F Sigmar fj), and use this basis to compute its dimension. In particular, we find a closed form formula for the dimension when r is a product of two primes, and when r is a prime power. It is known that the dimension of fj FSigmar fj is related to the number of standard Young tableau with major index congruent to j modulo r; therefore, the formula gives insight into this quantity as well.
Notlar:
School code: 0656
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(681910.1) | 681910-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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