Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups

Quasiregular representations of the infinite-dimensional nilpotent group

“…Let α(G) be the centralizer of the subgroup α(G) in Aut(X): α(G) = {g ∈ Aut(X) | {g, α t } = gα t g −1 α −1 t = e ∀t ∈ G}. The following conjecture has been discussed in [23][24][25].…”

“…In [25] it was shown that Conjecture 1 holds for the inductive limit G = SL 0 (2∞, R) = lim −→n SL(2n − 1, R), of the special linear groups (simple groups) acting on a strip of length m ∈ N in the space of real matrices which are infinite in both directions, the measure μ being a product Gaussian measure.…”

A Model with Interacting Assets Driven by Poisson Processes

“…We thank Alexandre Kosyak for very interesting discussions and for pointing out unpublished work by him [19], which was important for our investigations. The third named author gratefully acknowledges the hospitality of the Institute of Applied Mathematics of the University of Bonn and financial support by SFB 611, by the Alexander von Humboldt Foundation, by Caesar Institute (Bonn) and by the Summer Research Grant from Bentley College.…”

Quasiregular representations of the infinite-dimensional Borel group

“…In [27,28] the Conjecture 1 was proved for the nilpotent group G ¼ B N 0 and some G-spaces X m ; mAN; being the set of left cosets G m \B N ; where G m are some subgroups of the group B N : Here m is an arbitrary Gaussian product-measure on X m : In [29] it was shown that Conjecture 1 holds for the inductive limit G ¼ SL 0 ð2N; RÞ ¼ lim -n SLð2n À 1; RÞ; of the special linear groups (simple groups) acting on a strip of length mAN in the space of real matrices infinite in both directions, and the measure m being the product Gaussian measure.…”