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James’ regularization theorem for double covers of symmetric groups. (English) Zbl 1112.20009
Summary: This paper is concerned with the modular representation theory of Schur’s double covers of symmetric groups. We establish an analogue of James’ regularization theorem, which describes leading terms for branching multiplicities and decomposition numbers with respect to the usual dominance ordering.

MSC:
 20C30 Representations of finite symmetric groups 05E10 Combinatorial aspects of representation theory 20C20 Modular representations and characters
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References:
 [1] Brundan, J., Modular representations of the supergroup $$Q(n)$$, part II, Pacific J. math., 224, 65-90, (2006) · Zbl 1122.20022 [2] Brundan, J.; Kleshchev, A., Hecke – clifford superalgebras, crystals of type $$A_{2 \ell}^{(2)}$$ and modular branching rules for $$\hat{S}_n$$, Represent. theory, 5, 317-403, (2001) · Zbl 1005.17010 [3] Brundan, J.; Kleshchev, A., Projective representations of symmetric groups via sergeev duality, Math. Z., 239, 27-68, (2002) · Zbl 1029.20008 [4] Brundan, J.; Kleshchev, A., Modular representations of the supergroup $$Q(n)$$, I, J. algebra, 260, 64-98, (2003) · Zbl 1027.17004 [5] James, G.D., On the decomposition matrices of the symmetric groups. II, J. algebra, 43, 45-54, (1976) · Zbl 0347.20006 [6] James, G.D., The representation theory of the symmetric groups, Lecture notes in math., vol. 682, (1978), Springer-Verlag Berlin · Zbl 0393.20009 [7] Kleshchev, A., Linear and projective representations of symmetric groups, (2005), Cambridge Univ. Press Cambridge · Zbl 1080.20011 [8] Leclerc, B.; Thibon, J.-Y., q-deformed Fock spaces and modular representations of spin symmetric groups, J. phys. A, 30, 6163-6176, (1997) · Zbl 1039.17509 [9] Macdonald, I.G., Symmetric functions and Hall polynomials, Oxford math. monogr., (1995), Oxford Univ. Press · Zbl 0487.20007
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