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Partition identities and labels for some modular characters. (English) Zbl 0806.05065
The authors prove two conjectures on partitions which label the modular spin representations of the covering groups of the finite symmetric group \(S_ n\) in characteristic 5. Previous results were presented by the first author [On the general Rogers-Ramanujan theorem, Mem. Am. Math. Soc. 152 (1974; Zbl 0296.10010)], where also the second conjecture was stated in an equivalent form. The proofs involve a construction of polynomial generating functions which define the corresponding recurrence relations.
Reviewer: I.Strazdins (Riga)

MSC:
11P83 Partitions; congruences and congruential restrictions
20C25 Projective representations and multipliers
05A17 Combinatorial aspects of partitions of integers
05E10 Combinatorial aspects of representation theory
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