arXiv subjects
Publications and source records attributed to Chenglang Yang.
In this paper, we prove a conjecture of Alexandrov that the generalized Brezin-Gross-Witten tau-functions are hypergeometric tau functions of BKP hierarchy after re-scaling. In particular, this shows that the original BGW tau-function, which has enumerative geometric interpretations, can be represented as a linear combination of Schur Q-polynomials with simple coefficients.
Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints, and consequently obtain a proof of this formula without using matrix model. We also give a proof for Alexandrov's conjecture that Kontsevich-Witten tau-function is a hypergeometric tau-function of the BKP hierarchy after re-scaling.
We derive a formula for the connected $n$-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou in [arXiv:1507.01679]. Moreover, we prove a simple relation between the KP-affine coordinates of a tau-function $τ(\mathbf{t})$ of the KdV hierarchy and the BKP-affine coordinates of $τ(\mathbf{t}/2)$. As applications, we present a new algorithm to compute the free energies of the Witten-Kontsevich tau-function and the Brézin-Gross-Witten tau-function.
In this paper, we prove formulas for the action of Virasoro operators on Hall-Littlewood polynomials at roots of unity.