Block - Toeplitz Determinants
نویسنده
چکیده
We evaluate the Geiss-Leclerc-Schröer φ-map for shape modules over the preprojective algebra Λ of type c A1 in terms of matrix minors arising from the block-Toeplitz representation of the loop group SL2(L). Conjecturally these minors are among the cluster variables for coordinate rings of unipotent cells within SL2(L). In so doing we compute the Euler characteristic of any generalized flag variety attached to a shape module by counting standard tableaux of requisite shape and parity; alternatively by counting chess tableaux of requisite shape and content.
منابع مشابه
Block Toeplitz determinants , constrained KP and Gelfand - Dickey hierarchies
We propose a method for computing any Gelfand-Dickey τ function living in SegalWilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols W(t; z). Also truncated block Toeplitz determinants associated to the same symbols are shown to be τ function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from ...
متن کاملBlock Toeplitz operators with rational symbols
Toeplitz operators (or equivalently, Wiener-Hopf operators; more generally, block Toeplitz operators; and particularly, Toeplitz determinants) are of importance in connection with a variety of problems in physics, and in particular, in the field of quantum mechanics. For example, a study of solvable models in quantum mechanics uses the spectral theory of Toeplitz operators (cf. [Pr]); the one-d...
متن کاملFisher - Hartwig Formula and Entanglement entropy
Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use Fisher-Hartwig formula, as well as the recent results concerning the asymp-totics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in ...
متن کاملBoundary correlation function of fixed-to-free bcc operators in square-lattice Ising model
Abstract. We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using 2×2 block Toeplitz determinants. We show that these can be transformed into a scalar Toeplitz determinant when the size of the matrix is even. To know the asymptotic behavior of the c...
متن کامل. FA ] 1 J an 2 00 1 On the determinant formulas by Borodin , Okounkov , Baik , Deift , and Rains
We give alternative proofs to (block case versions of) some formulas for Toeplitz and Fredholm determinants established recently by the authors of the title. Our proof of the Borodin-Okounkov formula is very short and direct. The proof of the Baik-Deift-Rains formulas is based on standard manipulations with Wiener-Hopf factorizations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007