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Chenglang Yang

Publications and source records attributed to Chenglang Yang.

23 records · Page 2Linked to original sources
arXiv2023

Kac-Schwarz Operators of Type $B$, Quantum Spectral Curves, and Spin Hurwitz Numbers

Given a tau-function $τ(t)$ of the BKP hierarchy satisfying $τ(0)=1$, we discuss the relation between its BKP-affine coordinates on the isotropic Sato Grassmannian and its BKP-wave function. Using this result, we formulate a type of Kac-Schwarz operators for $τ(t)$ in terms of BKP-affine coordinates. As an example, we compute the affine coordinates of the BKP tau-function for spin single Hurwitz numbers with completed cycles, and find a pair of Kac-Schwarz operators $(P,Q)$ satisfying $[P,Q]=1$. By doing this, we obtain the quantum spectral curve for spin single Hurwitz numbers.

math-ph↗
arXiv2022

Q-Polynomial expansion for Brezin-Gross-Witten tau-function

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.

nlin.SI↗
arXiv2022

Schur Q-Polynomials and Kontsevich-Witten Tau Function

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.

math.AG↗
arXiv2022

BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions

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.

nlin.SI↗