526 research outputs found
On elementary proof of AGT relations from six dimensions
The actual definition of the Nekrasov functions participating in the AGT
relations implies a peculiar choice of contours in the LMNS and Dotsenko-Fateev
integrals. Once made explicit and applied to the original triply-deformed
(6-dimensional) version of these integrals, this approach reduces the AGT
relations to symmetry in q_{1,2,3}, which is just an elementary identity for an
appropriate choice of the integration contour (which is, however, a little
non-traditional). We illustrate this idea with the simplest example of N=(1,1)
U(1) SYM in six dimensions, however, all other cases can be evidently
considered in a completely similar way.Comment: 5 page
Ding-Iohara-Miki symmetry of network matrix models
Ward identities in the most general "network matrix model" can be described
in terms of the Ding-Iohara-Miki algebras (DIM). This confirms an expectation
that such algebras and their various limits/reductions are the relevant
substitutes/deformations of the Virasoro/W-algebra for (q, t) and (q_1, q_2,
q_3) deformed network matrix models. Exhaustive for these purposes should be
the Pagoda triple-affine elliptic DIM, which corresponds to networks associated
with 6d gauge theories with adjoint matter (double elliptic systems). We
provide some details on elliptic qq-characters.Comment: 20 pages, 2 figure
The MacMahon R-matrix
We introduce an -matrix acting on the tensor product of MacMahon
representations of Ding-Iohara-Miki (DIM) algebra
. This -matrix acts on pairs
of Young diagrams and retains the nice symmetry of the DIM algebra under
the permutation of three deformation parameters , and
. We construct the intertwining operator for a tensor product of
the horizontal Fock representation and the vertical MacMahon representation and
show that the intertwiners are permuted using the MacMahon -matrix.Comment: 39 page
Duality in elliptic Ruijsenaars system and elliptic symmetric functions
We demonstrate that the symmetric elliptic polynomials
originally discovered in the study of generalized Noumi-Shiraishi functions are
eigenfunctions of the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians that
act on the mother function variable (substitute of the Young-diagram
variable ). This means they are eigenfunctions of the dual eRS system.
At the same time, their orthogonal complements in the Schur scalar product,
are eigenfunctions of the elliptic reduction of the Koroteev-Shakirov
(KS) Hamiltonians. This means that these latter are related to the dual eRS
Hamiltonians by a somewhat mysterious orthogonality transformation, which is
well defined only on the full space of time variables, while the coordinates
appear only after the Miwa transform. This observation explains the
difficulties with getting the apparently self-dual Hamiltonians from the double
elliptic version of the KS Hamiltonians.Comment: 15 page
Time-consistency of cooperative solutions
Management in complex social and economics networks includes elements of cooperative behavior or full cooperation between agents involved in decision making process. The most appropriate mathematical tool for modeling in this case is the mathematical theory of cooperative games. Unfortunately the classical cooperative game theory considers cooperation as one-shot interaction between the decision makers and for this reason can not be used for modeling of dynamic interactions arising in long term strategic management. The theory of cooperative differential games is the most adequate tool for modeling strategic management development on a given time interval. The use of this theory from the beginning poses the problems connected with dynamic stability (time-consistency) of optimal cooperative solutions. The consideration of optimality principles taken from the classical cooperative game theory shows the time-inconsistency and thus non applicability of these principles in strategic management. In this paper the methods of construction of time consistent solutions is proposed for the problems of strategic management in social and economic networks. The authors tried to present a rather complicated material on acceptable level. Theory is illustrated with a number of examples and a more comprehensive analysis of joint venture.
Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.
The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.
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