Question

The following is from this talk: http://www.maths.usyd.edu.au/u/anthonyh/piecestalk.pdf, Slide 14.

The Springer correspondence gives bijections

SO2n+1 \ N(so2n+1) ↔ {(μ; ν) | μi ≥ νi − 2, νi ≥ μi+1},

Sp2n \ N(sp2n) ↔ {(μ; ν) | μi ≥ νi − 1, νi ≥ μi+1 − 1},

obtained from the previous parametrizations by taking 2-quotients.

What I don't understand, is given a partition of say, $2n$, that is symplectic (odd parts occur with even multiplicity), how to construct a bijection to the set above; and same with orthogonal partitions (even parts occur with even multiplicity).

Answer 1

From looking at the slides, it sure looks like you wrote it in your answer: take 2-quotients.

I'm not sure if there's a standard reference for n-quotients of partitions, but they're described in this paper, for example.