相关论文: Affine symmetries in quantum cohomology: correctio…
There are two intriguing statements regarding the quantum cohomology of partial flag varieties. The first one relates quantum cohomology to the affinisation of Lie algebras and the homology of the affine Grassmannian, the second one…
The Peterson isomorphism relates the homology of the affine Grassmannian to the quantum cohomology of any flag variety. In the case of a partial flag, Peterson's map is only a surjection, and one needs to quotient by a suitable ideal on the…
We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type A_n singularities. The operators encoding these invariants are expressed in terms of the…
We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and…
We give quantum Pieri rules for quantum cohomology of Grassmannians of classical types, expressing the quantum product of Chern classes of the tautological subbundles with general cohomology classes. We derive them by showing the relevant…
The cohomology of the affine flag variety of a complex reductive group is a comodule over the cohomology of the affine Grassmannian. We give positive formulae for the coproduct of an affine Schubert class in terms of affine Stanley classes…
We study the PI degree of various quantum algebras at roots of unity, including quantum Grassmannians, quantum Schubert varieties, partition subalgebras, and their associated quantum affine spaces. By a theorem of De Concini and Procesi,…
The Schubert bases of the torus-equivariant homology and cohomology rings of the affine Grassmannian of the special linear group are realized by new families of symmetric functions called k-double Schur functions and affine double Schur…
We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…
We show a Z^2-filtered algebraic structure and a "quantum to classical" principle on the torus-equivariant quantum cohomology of a complete flag variety of general Lie type, generalizing earlier works of Leung and the second author. We also…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
We give formulas for the products of classes of Schubert varieties in the quantum cohomology rings of Grassmannians, in terms of the combinatorics of partitions and tableaux.
A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric…
In this, the last of three papers about $C_2$-equivariant complex quadrics, we complete the calculation of the equivariant ordinary cohomology of smooth symmetric quadrics in the cases where the fixed sets have more than two components.…
We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C). Our main results are: 1) Pieri rules for the Schubert bases of H^*(Gr) and H_*(Gr), which expresses the product of a special…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
Using the Kontsevich's moduli space of stable maps, we define the equivariant quantum cohomology for generalized flag varieties and make a rigorous computation of quantum cohomology of flag varieties.