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Units of twisted group rings and their correlations to classical group rings
- Award ID(s):
- 1928930
- PAR ID:
- 10600021
- Publisher / Repository:
- ELSEVIER
- Date Published:
- Journal Name:
- Advances in Mathematics
- Volume:
- 458
- Issue:
- PB
- ISSN:
- 0001-8708
- Page Range / eLocation ID:
- 109983
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Given a representation of a finite group G over some commutative base ring k, the cofixed space is the largest quotient of the representation on which the group acts trivially. If G acts by k-algebra automorphisms, then the cofixed space is a module over the ring of G-invariants. When the order of G is not invertible in the base ring, little is known about this module structure. We study the cofixed space in the case that G is the symmetric group on n letters acting on a polynomial ring by permuting its variables. When k has characteristic 0, the cofixed space is isomorphic to an ideal of the ring of symmetric polynomials in n variables. Localizing k at a prime integer p while letting n vary reveals striking behavior in these ideals. As n grows, the ideals stay stable in a sense, then jump in complexity each time n reaches a multiple of p.more » « less
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