Equivariant Burnside groups and representation theory

Abstract

We apply the equivariant Burnside group formalism to distinguish linear actions of finite groups, up to equivariant birationality. Our approach is based on De Concini-Procesi models of subspace arrangements.

Equivariant Burnside groups and toric varieties

“…Symbols are also permitted in which K is a Galois algebra for some Y ⊆ Z over a field that is finitely generated over k; we identify (H, Y ý K, β) with (H, Z ý Ind Z Y (K), β). See [25] for a complete description of relations.…”

“…Here, • The induction homomorphism ind G G I,j : Burn n (G I,j ) → Burn n (G) is defined in [25,Defn. 3.1].…”

“…As a generalization of the map ψ I there is the map ψ I,J : Burn n,I (G) → Burn n,J (G), which appends just the characters indexed by elements of I \ J to the characters β; see [25,Defn. 4.2].…”

“…By analogy with [25,Conv. 8.1], here (O(−1)) denotes the following collection of line bundles, indexed by {1, .…”

“…In [19], [26] we studied various structural properties of this new invariant and provided first applications. In [25] we presented an algorithm to compute the classes of linear actions and presented examples of nonbirational such actions. Here, we turn to algebraic tori.…”