منابع مشابه
Quantum Jacobi-Trudi Formula and E8 Structure in the Ising Model in a Field
We investigate a 1D quantum system associated with the Ising model in a field(the dilute A3 model) by the recently developed quantum transfer matrix (QTM) approach. A closed set of functional relations is found among variants of fusion QTMs which are characterized by skew Young tableaux. These relations are proved by using a quantum analogue of Jacobi-Trudi formula, together with special featur...
متن کاملThe Smith normal form of a specialized Jacobi-Trudi matrix
Let JTλ be the Jacobi-Trudi matrix corresponding to the partition λ, so det JTλ is the Schur function sλ in the variables x1, x2, . . . . Set x1 = · · · = xn = 1 and all other xi = 0. Then the entries of JTλ become polynomials in n of the form ( n+j−1 j ) . We determine the Smith normal form over the ring Q[n] of this specialization of JTλ . The proof carries over to the specialization xi = q i...
متن کاملTerence Love1, PhD, Fellow DRS, Trudi Cooper2, PhD
This paper reports research into the application of Ashby’s Law of Requisite Variety to assist with identifying optimal choices of design solutions at the pre-design stage of designing digital ecosystems. This study of the application of Ashby’s Law is a component of a larger research program investigating the application of classical systems analysis tools in pre-design optimisation processes ...
متن کاملTwo parameters circular ensembles and Jacobi-Trudi type formulas for Jack functions of rectangular shapes
Jack function theory is useful for the calculation of the moment of the characteristic polynomials in Dyson’s circular β-ensembles (CβE). We define a q-analogue of the CβE and calculate moments of characteristic polynomials via Macdonald function theory. By this q-deformation, the asymptotics calculation of these moments becomes simple and the ordinary CβE case is recovered as q → 1. Further, b...
متن کاملPaths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type Dn
We study the Jacobi-Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type Dn. Unlike the An and Bn cases, a simple application of the Gessel-Viennot path method does not yield an expression of the determinant by a positive sum over a set of tuples of paths. However, apply...
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ژورنال
عنوان ژورنال: BMJ
سال: 2018
ISSN: 0959-8138,1756-1833
DOI: 10.1136/bmj.k2466