کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903787 | 1632917 | 2018 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On Hamiltonians for six-vertex models
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
We show that a deformation of Schur polynomials (matching the Shintani-Casselman-Shalika formula for the p-adic spherical Whittaker function) is obtained from a Hamiltonian operator on Fermionic Fock space. The discrete time evolution of this operator gives rise to states of a free-fermionic six-vertex model with boundary conditions generalizing the “domain wall boundary conditions,” which are not field-free. This is analogous to results of the Kyoto school in which ordinary Schur functions arise in the Boson-Fermion correspondence, and the Hamiltonian operator produces states of the five-vertex model. Our Hamiltonian arises naturally from super Clifford algebras studied by Kac and van de Leur. As an application, we give a new proof of a formula of Tokuyama [25] and Jacobi-Trudi type identities for the deformation of Schur polynomials. Variants leading to deformations of characters for other classical groups and their finite covers are also presented.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 155, April 2018, Pages 100-121
Journal: Journal of Combinatorial Theory, Series A - Volume 155, April 2018, Pages 100-121
نویسندگان
Ben Brubaker, Andrew Schultz,