Computations in generic representation theory: maps from symmetric powers to

composite functors

Author:
Nicholas J. Kuhn

Journal:
Trans. Amer. Math. Soc. **350** (1998), 4221-4233

MSC (1991):
Primary 20G05; Secondary 55S10, 55S12

DOI:
https://doi.org/10.1090/S0002-9947-98-02012-1

MathSciNet review:
1443197

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Abstract | References | Similar Articles | Additional Information

Abstract: If is the finite field of order and characteristic , let be the category whose objects are functors from finite dimensional -vector spaces to -vector spaces, and with morphisms the natural transformations between such functors. Important families of objects in include the families , and , with , defined by ,, , , and .

Fixing , we discuss the problem of computing , for all , given knowledge of for all . When , we get a complete answer for any functor chosen from the families listed above.

Our techniques involve Steenrod algebra technology, and, indeed, our most striking example, when , arose in recent work on the homology of iterated loopspaces.

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Additional Information

**Nicholas J. Kuhn**

Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903

Email:
njk4x@virginia.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-02012-1

Received by editor(s):
September 11, 1996

Received by editor(s) in revised form:
January 3, 1997

Additional Notes:
Partially supported by the N.S.F. and the C.N.R.S

Article copyright:
© Copyright 1998
American Mathematical Society