Zobrazeno 1 - 10
of 208
pro vyhledávání: '"Alexander Varchenko"'
Autor:
Alexander Varchenko
Publikováno v:
Mathematics, Vol 2, Iss 4, Pp 218-231 (2014)
We consider a weighted family of \(n\) generic parallelly translated hyperplanes in \(\mathbb{C}^k\) and describe the characteristic variety of the Gauss–Manin differential equations for associated hypergeometric integrals. The characteristic varie
Externí odkaz:
https://doaj.org/article/85eab188c78045cca615ff8395d1f9ce
Autor:
Alexander Varchenko
Publikováno v:
Mathematics, Vol 5, Iss 4, p 52 (2017)
We consider the Gauss–Manin differential equations for hypergeometric integrals associated with a family of weighted arrangements of hyperplanes moving parallel to themselves. We reduce these equations modulo a prime integer p and construct polynom
Externí odkaz:
https://doaj.org/article/69ca22bb0c474b3b9a9360b7a0b6c9fc
Autor:
Vitaly Tarasov, Alexander Varchenko
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 048 (2013)
We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian $Y({mathfrak{gl}}_N)$ and the quantum affine algebra~$U_q(widetilde{{mathfrak{gl
Externí odkaz:
https://doaj.org/article/404b2ce176b246a081e5df3737c5a3bb
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 8, p 072 (2012)
We discuss a relation between the characteristic variety of the KZ equations and the zero set of the classical Calogero-Moser Hamiltonians.
Externí odkaz:
https://doaj.org/article/9e850206274548ec82aa078aad7acaac
Autor:
Alexander Varchenko
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 7, p 032 (2011)
The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted arrangement of
Externí odkaz:
https://doaj.org/article/0c1c841f2b00467ba66847bf5d64c516
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 3, p 060 (2007)
Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = sum_{k=0}^N (-1)^k T_k(u) e^{-kpartial_u}$ whose coefficients $T_k(u): M o M$ are the XXX transfer ma
Externí odkaz:
https://doaj.org/article/e2ef6ef3b5de42c7a1e820c77e720b20
Autor:
Alexander Varchenko
Publikováno v:
Hypergeometry, Integrability and Lie Theory. :287-307
We consider the KZ differential equations over C \mathbb {C} in the case, when the hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field F p \mathbb {F}_p . We study the polynomia
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::994007622569df37abfbd232fa833544
https://doi.org/10.1090/conm/780/15694
https://doi.org/10.1090/conm/780/15694
Autor:
Alexander Varchenko
Publikováno v:
Hypergeometry, Integrability and Lie Theory. :309-347
We consider the differential KZ equations over C \mathbb C in the case, when the hypergeometric solutions are one-dimensional hyperelliptic integrals of genus g g . In this case the space of solutions of the differential KZ equations is a 2 g 2g -dim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::96ed80330c56ced0620433113376e674
https://doi.org/10.1090/conm/780/15695
https://doi.org/10.1090/conm/780/15695
Autor:
Alexander Varchenko, Vitaly Tarasov
Publikováno v:
European Journal of Mathematics. 7:706-728
We consider the equivariant quantum differential equation for the projective space $$P^{n-1}$$ and introduce a compatible system of difference equations. We prove an equivariant gamma theorem for $$P^{n-1}$$ , which describes the asymptotics of the d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a0329aee7c8206ed5d245beb1d6ff9ed
https://doi.org/10.1007/s40879-021-00455-y
https://doi.org/10.1007/s40879-021-00455-y
Autor:
Alexander Varchenko
Publikováno v:
Mathematical Notes. 109:386-397
We consider the KZ differential equations over $$\mathbb C$$ in the case where its multidimensional hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $$\mathbb{F}_p$$ . We stu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5a024e13a3de2bc4ededf830c9d09226
https://doi.org/10.1134/s0001434621030068
https://doi.org/10.1134/s0001434621030068