Related papers: t-deformation of quantum Schubert polynomials
We describe the quantum cohomology rings of a class of toric varieties. The description includes, in addition to the (already known) ring presentations, the (new) analogues for toric varieties of the sorts of quantum Giambelli formulas…
Using the Baxter's T-Q relation derived from the transfer matrix technique, we consider the diagonalization problem of discrete quantum pendulum and discrete quantum sine-Gordon Hamiltonian from the algebraic geometry aspect. For a finite…
Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square…
We provide a method for gluing (small) resolutions of singularities of Schubert varieties \(X_w\). An explicit isomorphism of \(X_w\) with an (iterated) bundle is constructed when \(w\) has an (iterated) BP decomposition. Combined with the…
The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \lambda(\phi)=0,…
A simple method is proposed for deforming $A_\infty$-algebras by means of the resolution technique. The method is then applied to the associative algebras of polynomial functions on quantum superspaces. Specifically, by introducing suitable…
We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…
We describe the integral cohomology rings of the flag manifolds of types B_n, D_n, G_2 and F_4 in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an…
We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the…
We perform the dynamical change of coordinates to derive a generalization of the trace relation and apply it to the non-linear Schr\"odinger model. After that, we work out the dimensional reduction of the bilinear $T\bar T$ operator and…
We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…
The quantum group version of the Bernstein-Gelfand-Gelfand resolution is used to construct a double complex of U_q(g)-modules with exact rows and columns. The locally finite dual of its total complex is identified with the de Rham complex…
We use incidence relations running in two directions in order to construct a Kempf-Laksov type resolution for any Schubert variety of the complete flag manifold but also an embedded resolution for any Schubert variety in the Grassmannian.…
We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant…
We investigate the quantum deformation of the Wheeler--DeWitt equation of a Schwarzchild black hole. Specifically, the quantum deformed black hole is a quantized model constructed from the quantum Heisenberg--Weyl $U_q(h_4)$ group. We show…
This work investigates the vertical quantum cohomology and quantum spectra of flag bundles, uncovering new links between the Gromov-Witten theory of homogeneous fibrations and analytic number theory. Building on previous constructions by…
We show that reductions of KP hierarchies related to the loop algebra of $SL_n$ with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to…
Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class…
We consider the system of quantum differential equations for a partial flag variety and construct a basis of solutions in the form of multidimensional hypergeometric functions, that is, we construct a Landau-Ginzburg mirror for that partial…
We employ holography to calculate the quantum complexity of $T\bar{T}$-deformation, utilizing the complexity equals volume (CV) and the complexity equals action (CA) proposals within the bulk spacetime with a finite radius cutoff. We find…