共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
S. M. Arkhipov 《Communications in Mathematical Physics》1997,188(2):379-405
We define a new cohomology theory of associative algebras called semiinfinite cohomology in the derived categories' setting.
We investigate the case of a small quantum group u, calculate semiinfinite cohomology spaces of the trivial u-module and express them in terms of local cohomology of the nilpotent cone for the corresponding semisimple Lie algebra.
We discuss the connection between the semiinfinite homology of u and the conformal blocks' spaces.
Received: 14 October 1996 / Accepted: 25 February 1997 相似文献
3.
Christian Korff 《Letters in Mathematical Physics》2014,104(7):771-810
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged \({\mathfrak{\hat{u}}(n)_{k}}\) -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra. 相似文献
4.
We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag
manifold (an infinite-dimensional K?hler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice
and the quantum cohomology of the finite-dimensional flag manifold. We derive a simple and explicit “differential operator
formula” for the necessary quantum products, which applies both to the finite-dimensional and to the infinite-dimensional
situations.
Received: 20 April 1999 / Accepted: 12 April 2000 相似文献
5.
Krzysztof Gawȩdzki Rafał R. Suszek Konrad Waldorf 《Communications in Mathematical Physics》2008,284(1):1-49
The simplest orientifolds of the WZW models are obtained by gauging a symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion , where ζ is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold
theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups
that combine the -action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to
a problem in group-Γ cohomology that we solve for all simple simply connected compact Lie groups G and all orientifold groups .
Membre du C.N.R.S. 相似文献
6.
Vadim Schechtman 《Communications in Mathematical Physics》1999,208(2):355-379
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant
pseudo-K?hler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant
symbols.
Received: 5 August 1997 / Accepted: 8 July 1998 相似文献
7.
We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping
class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first
universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion .
L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311. 相似文献
8.
Davide Guzzetti 《Communications in Mathematical Physics》1999,207(2):341-383
In this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be
formulated in a “classical” framework, as the problem of computation of Stokes matrices and monodromy of differential equations
with regular and irregular singularities. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram
matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology
and we show that it is related to hyperbolic triangular groups.
Received: 24 October 1998 / Accepted: 27 April 1999 相似文献
9.
We propose an algebraic scheme for quantizing the rational Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special parametrization of the cotangent bundle over . In new variables the standard symplectic structure is described by a classical (Frobenius) r-matrix and by a new dynamical -matrix. Quantizing both of them we find the quantum L-operator algebra and construct its particular representation corresponding to the rational Ruijsenaars-Schneider system.
Using the dual parametrization of the cotangent bundle we also derive the algebra for the L-operator of the hyperbolic Calogero-Moser system.
Received: 24 January 1997 / Accepted: 17 March 1997 相似文献
10.
11.
We give an explicit procedure which computes for degree d≤ 3 the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface X as homogeneous polynomials of degree d in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi–Yau hypersurfaces
and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which
express the structure constants of the quantum cohomology ring of X as weighted homogeneous polynomial functions of the constants of the Fano hypersurface with the same degree and dimension
one more. We propose some conjectures about the existence and the form of the recursive laws for the structure constants of
rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used
in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree
four.
Received: 29 November 1996 / Accepted: 15 March 1999 相似文献
12.
13.
Xing-Chang SONG 《理论物理通讯》1994,21(2):173-180
From the basic 4 × 4 R matrix associated with the quantum Lorentz group SLq(2, C) and its various fusion matrices, the covariant differential calculus on the quantum Minkowski space and the R commutation relation for the covariant generators of quantum Lorents group are presented. 相似文献
14.
We generalize some of the standard homological techniques toW-algebras, and compute the semi-infinite cohomology of theW
3 algebra on a variety of modules. These computations provide physical states inW
3 gravity coupled toW
3 minimal models and to two free scalar fields.Supported by the Packard Foundation.Supported by the Australian Research Council.Supported in part by the Department of Energy Contract # DE-FG03-84ER-40168. 相似文献
15.
We study the equilibrium statistical mechanics of the semi-infinite Ising model, interpreted as a model of a binary system near a wall. In particular, the wetting transition is analyzed. In dimensionsd3 and at low temperature, we prove the existence of a layering transition which is of first-order.Dedicated to Walter Thirring on his 60th birthday 相似文献
16.
We use previous work on the chiral de Rham complex and Borisov's deformation of a lattice vertex algebra to give a simple
linear algebra construction of quantum cohomology of toric varieties. Somewhat unexpectedly, the same technique allows to
compute the formal character of the cohomology of the chiral de Rham complex on even dimensional projective spaces. In particular,
we prove that the formal character of the space of global sections equals the equivariant signature of the loop space, a well-known
example of the Ochanine-Witten elliptic genus.
Received: 15 July 2000 / Accepted: 17 August 2002 Published online: 8 January 2003
RID="*"
ID="*" Partially supported by an NSF grant
Communicated by R. H. Dijkgraaf 相似文献
17.
For the semi-infinite Ising model in two or more dimensions, we prove analyticity properties of the surface free energy and map out the phase diagram in the absence of an external magnetic field. We prove that this phase diagram contains critical lines where the parallel and/or the transverse correlation lengths diverge. The critical exponent,v ⊥, of the transverse correlation length is shown to be equal to the exponentv of the Ising model on an infinite lattice. In a second paper, these results will be used to analyze the wetting transition. 相似文献
18.
Giovanni Landi 《Letters in Mathematical Physics》2006,75(2):187-200
We construct a model of spin-Hall effect on a noncommutative four sphere S
4
Θ with isospin degrees of freedom, coming from a noncommutative instanton, and invariance under a quantum group SO
θ. The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state;
there are both integer and fractional excitations. Similar models exist on higher dimensional spheres S
Θ
N
and projective spaces
.
Dedicated to Rafael Sorkin with friendship and respect. 相似文献
19.
General theory of quantum statistics with internal degree of freedom in two dimensions is studied. Because of the topological nontrivial properties in the configuration space of indistinguishable particles, the intrinsic part of many-body wave function is associated with the representation of quantum group, which describes θ statistics. The statistical potential and the effective Hamiltonian of general two-dimensional system can be derived from the Kohno connection. 相似文献
20.
LI Min-Si LIU Yan-Na 《理论物理通讯》2008,50(8):517-520
We show that there is a quantum Slq(2) group symmetry in Hofstadter problem on square lattice. The cyclic representation of the quantum group is discussed and its application for computing the degeneracy density of the model is shown. 相似文献