You are cordially invited to the Algebra Seminar organized by the Department of Mathematics.
Speaker: Müfit Sezer (Bilkent)
“Vector invariants of permutation groups in characteristic zero”
Abstract: We consider a finite permutation group acting naturally on a vector space V over a field k. A well-known theorem of Göbel asserts that the corresponding ring of invariants k[V]^G is generated by invariants of degree at most binom{dim V}{2}. In this note we show that if the characteristic of k is zero then the top degree of vector coinvariants k[V^m]_G is also bounded above by binom{dim V}{2}, which implies the degree bound binom{dim V}{2}+ 1 for the ring of vector invariants k[V^m]^G. So Göbel’s bound almost holds for vector invariants in characteristic zero as well. This is a joint work with F. Reimers.
Date: Monday, November 27, 2023
Time: 10:30
Place: SA141 – Mathematics Seminar Room