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Dickson–Mui Invariants
Author(s) -
Crabb M. C.
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004704
Subject(s) - subring , mathematics , invariant (physics) , vector space , mathematics subject classification , pure mathematics , algebra over a field , covariant transformation , field (mathematics) , ring (chemistry) , mathematical physics , chemistry , organic chemistry
Let V be a finite‐dimensional vector space over a finite field. The general and special linear groups, GL( V ) and SL( V ), act on the exterior algebras Λ * V and Λ * V * of V and its dual V * , and on the symmetric algebra S * V . The subring of SL( V )‐invariants of Λ * V ⊗S * V was determined by Dickson and Mui. This paper describes the equivalent, but simpler, calculation of the invariant subring of Λ * V ⊗S * V as a representation of GL( V )/SL( V ). 2000 Mathematics Subject Classification 13A50.