Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
The Cohomology Of The Steendrod Algebra And Representations Of The General Linear Groups, Nguyen H. V. Hu'ng
The Cohomology Of The Steendrod Algebra And Representations Of The General Linear Groups, Nguyen H. V. Hu'ng
Mathematics Research Reports
Let Tr_k be the algebraic transfer that maps from the coinvariants of certain GL_k-representation to the cohomology of the Steenrod algebra. This transfer was defined by W. Singer as an algebraic version of the geometrical transfer tr_k : pi_*^S((B[doublestrike V]_k)_+) --> pi_*^S(S^0). It has been shown that the algebraic transfer is highly nontrivial, more precisely, that Tr_k is an isomorphism for k = 1, 2, 3 and that T_r = ⊕_k(Tr_k) is a homomorphism of algebras.
In this paper, we first recognize the phenomenon that if we start from any degree d, and apply Sq^0 repeatedly at most (k- 2) …