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An integral second fundamental theorem of invariant theory for partition algebras.
- Source :
- Representation Theory; 2022, Vol. 26, p437-454, 18p
- Publication Year :
- 2022
-
Abstract
- We prove that the kernel of the action of the group algebra of the Weyl group acting on tensor space (via restriction of the action from the general linear group) is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra over an arbitrary commutative ring and proves that the centraliser algebras of the partition algebra are cellular. We also prove similar results for the half partition algebras. [ABSTRACT FROM AUTHOR]
- Subjects :
- GROUP algebras
ALGEBRA
WEYL groups
COMMUTATIVE rings
INTEGRALS
Subjects
Details
- Language :
- English
- ISSN :
- 10884165
- Volume :
- 26
- Database :
- Complementary Index
- Journal :
- Representation Theory
- Publication Type :
- Academic Journal
- Accession number :
- 156073803
- Full Text :
- https://doi.org/10.1090/ert/593