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We present a generic derivation of the WDVV equations for 6d Seiberg–Witten theory, and extend it to the families of bi-elliptic spectral curves. We find that the elliptization of the naive perturbative and nonperturbative 6d systems roughly “doubles” the number of moduli describing the system.
Deforming commutative algebras in the lower triangular (ℤ×ℤ)-matrices yields lower triangular Toda hierarchies and their associated nonlinear equations. Like for their counterpart in the ring of pseudodifferential operators, the KP-hierarchy, one also has for these hierarchies a geometric...
We construct a family of special quasigraded Lie algebras
of functions of one complex variables with values in finite-dimensional Lie algebra
, labeled by the special 2-cocycles F on
. The main property of the constructed Lie...
This is a brief review of my recent works with B. Enriquez on the relations between Hitchin and Beauville-Mukai algebraically completely integrable systems (ACIS) with emphasis on the quantization of their birational correspondence. The second part of the contribution gives an example of the...
We present some formulas for the computation of the zeros of the integral-degree associated Legendre functions with respect to the order.
We present a finite-dimensional system of discrete orthogonality relations for the Hall-Littlewood polynomials. A compact determinantal formula for the weights of the discrete orthogonality measure is formulated in terms of a Gaudin-type conjecture for the normalization constants of a dual...
We establish relations between Maurer–Cartan forms of symmetry pseudo-groups and coverings of differential equations. Examples include Liouville’s equation, the Khokhlov–Zabolotskaya equation, and the Boyer–Finley equation.
We define canonical representations R
, for the Lobachevsky space ℒ=G/K of dimension n−1 where G=SO0(n−1,1), K=SO(n−1), as the restriction to G of maximal degenerate series representations of the overgroup
. We determine...
Symmetric spaces or more general symmetric k-varieties can be defined as the homogeneous spaces G
, where G is a reductive algebraic group defined over a field k of characteristic not 2, K the fixed point group of an involution θ of G and G
the sets k-rational points of...
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