There is a well-known orthogonality property of U(N) group characters
∫dUχμ(U)χλ(U†V)=δμλχμ(V)dimμ
where the integral is over unitary group, χλ is a character, labeled by the partition λ and dimμ is the dimension of the correspondent representation, namely dimλ=χλ(1), the value of the character on the trivial group element.
In mathematical physics, in particular in topological strings (for example topological vertex) there appears the q-deformation of the dimension, namely dimqλ=χλ(ρ)
where ρ is the diagonal matrix with the entries 1,q,q2,…. The question:
is there any natural deformation of the unitary integral, which gives q-deformed dimensions in the r.g.s.?
[∫dU]qχμ(U)χλ(U†V)=δμλχμ(V)dimqμ
This post imported from StackExchange MathOverflow at 2014-07-28 11:17 (UCT), posted by SE-user Sasha