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no. 6
Composition factors of 2-parts spin representations of symmetric groups
Morotti, Lucia1
1 Institut für Algebra, Zahlentheorie und Diskrete Mathematik Leibniz Universität Hannover 30167 Hannover Germany
Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1283-1291.

Given an odd prime p, we identify possible composition factors of the reduction modulo p of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.137
Classification: 20C30, 20C25, 20C20
Keywords: Symmetric groups, spin representations, decomposition numbers.

Morotti, Lucia 1

1 Institut für Algebra, Zahlentheorie und Diskrete Mathematik Leibniz Universität Hannover 30167 Hannover Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Morotti, Lucia. Composition factors of 2-parts spin representations of symmetric groups. Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1283-1291. doi : 10.5802/alco.137. https://alco.centre-mersenne.org/articles/10.5802/alco.137/

[1] Andrews, George E.; Bessenrodt, Christine; Olsson, Jørn B. Partition identities and labels for some modular characters, Trans. Amer. Math. Soc., Volume 344 (1994), pp. 597-615 | DOI | MR | Zbl

[2] Benson, Dave Spin modules for symmetric groups, J. London Math. Soc. (2), Volume 38 (1988), pp. 250-262 | DOI | MR | Zbl

[3] Bessenrodt, Christine Representations of the covering groups of the symmetric groups and their combinatorics, Sém. Lothar. Combin., Volume 33 (1994), Paper no. Art. B33a, 29 pages | MR | Zbl

[4] Bessenrodt, Christine; Morris, Alun O.; Olsson, Jørn B. Decomposition matrices for spin characters of symmetric groups at characteristic 3, J. Algebra, Volume 164 (1994) no. 1, pp. 146-172 | DOI | MR | Zbl

[5] Bessenrodt, Christine; Olsson, Jørn B. The 2-blocks of the covering groups of the symmetric groups, Adv. Math., Volume 129 (1997) no. 2, pp. 261-300 | DOI | MR | Zbl

[6] Brundan, Jonathan; Kleshchev, Alexander Hecke–Clifford superalgebras, crystals of type A 2l (2) and modular branching rules for S ^ n , Represent. Theory, Volume 5 (2001), pp. 317-403 | DOI | MR | Zbl

[7] Brundan, Jonathan; Kleshchev, Alexander Projective representations of symmetric groups via Sergeev duality, Math. Z., Volume 239 (2002) no. 1, pp. 27-68 | DOI | MR | Zbl

[8] Brundan, Jonathan; Kleshchev, Alexander Modular representations of the supergroup Q(n). I, J. Algebra, Volume 260 (2003) no. 1, pp. 64-98 | DOI | MR | Zbl

[9] Brundan, Jonathan; Kleshchev, Alexander James’ regularization theorem for double covers of symmetric groups, J. Algebra, Volume 306 (2006) no. 1, pp. 128-137 | DOI | MR | Zbl

[10] Fayers, Matthew Defect 2 spin blocks of symmetric groups and canonical basis coefficients (2019) (https://arxiv.org/abs/1905.04080)

[11] James, Gordon D. On the decomposition matrices of the symmetric groups. I, J. Algebra, Volume 43 (1976) no. 1, pp. 42-44 | DOI | MR

[12] Kleshchev, Alexander Linear and projective representations of symmetric groups, Cambridge Tracts in Mathematics, 163, Cambridge University Press, Cambridge, 2005, xiv+277 pages | DOI | MR | Zbl

[13] Kleshchev, Alexander; Shchigolev, Vladimir Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n), Mem. Amer. Math. Soc., Volume 220 (2012) no. 1034, p. xviii+123 | DOI | MR | Zbl

[14] Leclerc, Bernard; Thibon, Jean-Yves q-deformed Fock spaces and modular representations of spin symmetric groups, J. Phys. A, Volume 30 (1997) no. 17, pp. 6163-6176 | DOI | MR | Zbl

[15] Morris, Alun O.; Yaseen, A. K. Decomposition matrices for spin characters of symmetric groups, Proc. Roy. Soc. Edinburgh Sect. A, Volume 108 (1988), pp. 145-164 | DOI | MR | Zbl

[16] Müller, Jürgen Brauer trees for the Schur cover of the symmetric group, J. Algebra, Volume 266 (2003) no. 2, pp. 427-445 | DOI | MR | Zbl

[17] Wales, David B. Some projective representations of S n , J. Algebra, Volume 61 (1979) no. 1, pp. 37-57 | DOI | MR | Zbl

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