RELATING TENSOR STRUCTURES ON REPRESENTATIONS OF GENERAL LINEAR AND SYMMETRIC GROUPS

For polynomial representations of GL n of a fixed degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring k , the Schur functor carries this internal tensor product to the usual Kronecker tensor...

Full description

Saved in:
Bibliographic Details
Published in:Transformation groups 2018-06, Vol.23 (2), p.437-461
Main Authors: KULKARNI, UPENDRA, SRIVASTAVA, SHRADDHA, SUBRAHMANYAM, K. V.
Format: Article
Language:English
Subjects:
Algebra
Group theory
Homology
Lie Groups
Mathematics
Mathematics and Statistics
Polynomials
Representations
Topological Groups
Traveling salesman problem
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For polynomial representations of GL n of a fixed degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring k , the Schur functor carries this internal tensor product to the usual Kronecker tensor product of symmetric group representations. This is true even at the level of derived categories. The new tensor product is a substantial enrichment of the Kronecker tensor product. E.g., in modular representation theory it brings in homological phenomena not visible on the symmetric group side. We calculate the internal tensor product over any commutative ring k in several interesting cases involving classical functors and the Weyl functors. We show an application to the Kronecker problem in characteristic zero when one partition has two rows or is a hook.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-018-9481-x