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Polynomiality of projective modular representations graded rings. (English) Zbl 1480.20040

Summary: Consider the Grothendieck group of finite type projective modular representations of the symmetric groups on \(n\) letters, or more generally, of its wreath product with a finite group. They form a graded group, with a product defined using induction. We show that the resulting graded ring is a polynomial ring.

MSC:

20C30 Representations of finite symmetric groups
20C20 Modular representations and characters
20E22 Extensions, wreath products, and other compositions of groups
16W50 Graded rings and modules (associative rings and algebras)
16T05 Hopf algebras and their applications
05E05 Symmetric functions and generalizations

Software:

reps; SageMath; GAP
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Full Text: DOI

References:

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