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16 votes
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Majorization and Schur Polynomials

This question is listed as a conjecture (conjecture 7.4 in the section "Open questions") in a recent paper of Cuttler, Greene and Skandera.
Vladimir Dotsenko's user avatar
13 votes
1 answer
1k views

Irreducibility of Schur polynomials

A natural question covering both this and this question would be Let $n>2$. Describe Young diagrams $\lambda$ with at most $n$ nonempty rows (or equivalently non-increasing sequences $\lambda=(\lamb …
Vladimir Dotsenko's user avatar
7 votes

Applying $\sum_i \partial_{x_i}$, $\sum_i x_i \partial_{x_i}$ and $\sum_i x_i^2 \partial_{x_...

The answer for $L_1=\sum_ix_i^2\partial_i$ can be derived in a rather straightforward way (I changed your convention a little bit to match the usual formulas for Virasoro algebra). Namely, use the det …
Vladimir Dotsenko's user avatar