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Найдены 23 публикации
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Статья
Takebe T., Teo L. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2006. Vol. 2. No. 072. P. 1-30.
Добавлено: 13 августа 2014
Статья
Takebe T. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2014. Vol. 10. P. 1-13.

We show that N-variable reduction of the dispersionless BKP hierarchy is described by a Loewner type equation for the quadrant.

Добавлено: 15 марта 2014
Статья
Burman Y. M., Berenstein A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2009. Vol. 5. No. 57. P. 1-18.

Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.

Добавлено: 12 октября 2012
Статья
Khoroshkin S. M., Пакуляк С. З. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2008. Vol. 4. No. 081. P. 23.
Добавлено: 15 октября 2012
Статья
Levin A., Olshanetsky M., Smirnov A. V. et al. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2012. Vol. 8. No. 095.
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different topological types over complex curves Sigma(g,n) of genus g with n marked points. The bundles are defined by their characteristic classes - elements of H-2 (Sigma(g,n), Z(G)), where Z (G) is a center of the simple complex Lie group G. The KZB equations are the horizontality condition for the projectively flat connection (the KZB connection) defined on the bundle of conformal blocks over the moduli space of curves. The space of conformal blocks has been known to be decomposed into a few sectors corresponding to the characteristic classes of the underlying bundles. The KZB connection preserves these sectors. In this paper we construct the connection explicitly for elliptic curves with marked points and prove its flatness.
Добавлено: 7 февраля 2013
Статья
Nirov Khazret S., Razumov A. V. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2017. Vol. 13. No. 043. P. 1-31.
Добавлено: 29 января 2018
Статья
Loktev S., Natanzon S. M. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2011. Vol. 7. No. 70. P. 1-15.

We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.

Добавлено: 12 октября 2012
Статья
Rybnikov L. G., Chervov A., Falqui G. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2009. Vol. 5. No. 29. P. 17.
We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals(in the classical case) and new “Gaudin” algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed(in the classical case). We will make use of properties of “Manin matrices” to provide explicit generators of the Gaudin Algebras in the quantum case.
Добавлено: 12 октября 2012
Статья
Spiridonov V., Magadov K. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2018. Vol. 14. No. 121. P. 1-13.
Добавлено: 14 ноября 2018
Статья
Akhtar M., Coates T., Galkin S. et al. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2012. Vol. 8. No. 094. P. 1-707.

Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Laurent polynomials in two variables; they preserve the period and are closely connected with cluster algebras. We propose a higher-dimensional analog of mutation acting on Laurent polynomials f in n variables. In particular we give a combinatorial description of mutation acting on the Newton polytope P of f, and use this to establish many basic facts about mutations. Mutations can be understood combinatorially in terms of Minkowski rearrangements of slices of P, or in terms of piecewise-linear transformations acting on the dual polytope P* (much like cluster transformations). Mutations map Fano polytopes to Fano polytopes, preserve the Ehrhart series of the dual polytope, and preserve the period of f. Finally we use our results to show that Minkowski polynomials, which are a family of Laurent polynomials that give mirror partners to many three-dimensional Fano manifolds, are connected by a sequence of mutations if and only if they have the same period.

Добавлено: 14 сентября 2013
Статья
Zotov A., Levin A., Olshanetsky M. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2009. Vol. 5. No. 065. P. 1-22.
Modifications of bundles over complex curves is an operation that allows one to construct a new bundle from a given one. Modifications can change a topological type of bundle. We describe the topological type in terms of the characteristic classes of the bundle.Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. Following Kapustin and Witten we define the modifications in terms of monopole solutions of the Bogomolny equation. We find the Dirac monopole solution in the case R × (elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it generalizing the Kronecker results. We use it to define Abelian modifications for bundles of arbitrary rank. We also describe non-Abelian modifications in terms of thetafunctions with characteristic.
Добавлено: 15 октября 2012
Статья
Hutsalyuk A., Liashyk A., Pakuliak S. et al. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2016. Vol. 12. No. 099. P. 1-22.
Добавлено: 17 ноября 2016
Статья
Kirillov A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2016. Vol. 12.

We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco-Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.

Добавлено: 5 мая 2016
Статья
Ayano T., Nakayashiki A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2013. Vol. 9. No. 046.
Добавлено: 2 ноября 2016
Статья
Ayano T. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2016. Vol. 12. No. 086.
Добавлено: 2 ноября 2016
Статья
Gavrylenko P., Iorgov N., Lisovyy O. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2018. Vol. 14. P. 1-27.
Добавлено: 22 ноября 2018
Статья
Ogievetsky O., Khoroshkin S. M. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2011. Vol. 7. No. 64. P. 1-34.
We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra gl n into gl n ⊕gl n . Its representation theory is related to the theory of decompositions of tensor products of gl n -modules.
Добавлено: 15 октября 2012
Статья
Pogrebkov A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2017. Vol. 13. No. 53. P. 1-14.
Добавлено: 4 сентября 2017
Статья
Sergeev A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2009. Vol. 5. No. 015. P. 1-20.
Добавлено: 19 февраля 2013
Статья
Bizyaev I. A., Borisov A. V., Mamaev I. S. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2016. Vol. 12. P. 1-19.
Добавлено: 5 апреля 2017
Статья
Zabrodin A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2014. Vol. 10. No. 006. P. 18.
Добавлено: 15 июля 2014
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