Zobrazeno 1 - 10
of 169
pro vyhledávání: '"Harnad, J. P."'
Autor:
Harnad, J.
The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank, is derived
Externí odkaz:
http://arxiv.org/abs/2308.01892
Publikováno v:
J. Math. Phys. 64, 083502 (2023)
The Hamiltonian approach to isomonodromic deformation systems is extended to include generic rational covariant derivative operators on the Riemann sphere with irregular singularities of arbitrary Poincar\'e rank. The space of rational connections wi
Externí odkaz:
http://arxiv.org/abs/2212.06880
Publikováno v:
J. Math. Phys. 64, 023502 (2023)
The addition formulae for KP $\tau$-functions, when evaluated at lattice points in the KP flow group orbits in the infinite dimensional Sato-Segal-Wilson Grassmannian, give infinite parametric families of solutions to discretizations of the KP hierar
Externí odkaz:
http://arxiv.org/abs/2207.08054
Publikováno v:
Commun. Math. Phys. 401, 1337-1381 (2023)
This work concerns the relation between the geometry of Lagrangian Grassmannians and the CKP integrable hierarchy. The Lagrange map from the Lagrangian Grassmannian of maximal isotropic (Lagrangian) subspaces of a finite dimensional symplectic vector
Externí odkaz:
http://arxiv.org/abs/2202.13991
Publikováno v:
Ann. H. Poincar\'e, 23, 4521- 4554 (2022)
We extend the approach to ${\tau}$-functions as Widom constants developed by Cafasso, Gavrylenko and Lisovyy to orthogonal loop group Drinfeld-Sokolov hierarchies and isomonodromic deformations systems. The combinatorial expansion of the ${\tau}$-fun
Externí odkaz:
http://arxiv.org/abs/2112.12666
Autor:
Harnad, J., Orlov, A. Yu.
Publikováno v:
Annales Henri Poincar\'e 22, 3025-3049 (2021)
Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations of Jacobi's
Externí odkaz:
http://arxiv.org/abs/2011.13339
Bilinear expansions of lattices of KP $\tau$-functions in BKP $\tau$-functions: a fermionic approach
Autor:
Harnad, J., Orlov, A. Yu.
Publikováno v:
J. Math. Phys. 62, 013508 (2021)
We derive a bilinear expansion expressing elements of a lattice of KP $\tau$-functions, labelled by partitions, as a sum over products of pairs of elements of an associated lattice of BKP $\tau$-functions, labelled by strict partitions. This generali
Externí odkaz:
http://arxiv.org/abs/2010.05055
Autor:
Harnad, J., Orlov, A. Yu.
Publikováno v:
Proc. Amer. Math. Soc. 149, 4117-4131 (2021)
An identity is derived expressing Schur functions as sums over products of pairs of Schur $Q$-functions, generalizing previously known special cases. This is shown to follow from their representations as vacuum expectation values (VEV's) of products
Externí odkaz:
http://arxiv.org/abs/2008.13734
Publikováno v:
J. Math. Phys. 62, 021701 (2021)
This work is motivated by the relation between the KP and BKP integrable hierarchies, whose $\tau$-functions may be viewed as sections of dual determinantal and Pfaffian line bundles over infinite dimensional Grassmannians. In finite dimensions, we s
Externí odkaz:
http://arxiv.org/abs/2007.03586