An integral Riemann-Roch formula for induced representations of finite groups

Authors:
Leonard Evens and Daniel S. Kahn

Journal:
Trans. Amer. Math. Soc. **245** (1978), 331-347

MSC:
Primary 55R40; Secondary 20C99

DOI:
https://doi.org/10.1090/S0002-9947-1978-0511413-4

MathSciNet review:
511413

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *H* be a subgroup of the finite group *G*, a finite dimensional complex representation of *H* and the induced representation of *G*. If , denote the characteristic classes bearing the same relation to power sums that Chern classes bear to elementary symmetric functions, then we prove the following,

(1) |

where

(2) |

and

(3) |

(Tr denotes transfer.) Moreover, is the least integer with this property.

This settles a question originally raised in a paper of Knopfmacher in which it was conjectured that the required bound was *N(k)*.

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0511413-4

Keywords:
Characteristic class,
Chern class,
Knopfmacher,
Riemann-Roch formula,
induced representation,
group,
transfer,
wreath product

Article copyright:
© Copyright 1978
American Mathematical Society