Canonical Forms of Differential Equations Free from Accessory Parameters

Haraoka, Yoshishige

doi:10.1137/s0036141092231082

Cited by 17 publications

(16 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the cases of type ðIIÞ 2n and ðIIIÞ 2nþ1 , the following canonical forms of the Okubo systems are proposed by Haraoka [1].…”

Section: Okubo Systems Of Types I Imentioning

confidence: 99%

“…This lemma is essentially used in [1] for the construction of canonical forms. The explicit forms of x and h described above can also be derived by the property of Cauchy matrices as in [1].…”

Section: Construction Of Canonical Forms Of the Okubo Systems Of Typementioning

confidence: 99%

“…The explicit forms of x and h described above can also be derived by the property of Cauchy matrices as in [1]. From ðIIÞ 2n to ðIIIÞ 2nþ1 Similarly one can construct the canonical form (2.16) of the Okubo system ðIIÞ 2nþ2 from ðIIIÞ 2nþ1 by the middle convolution.…”

Section: Construction Of Canonical Forms Of the Okubo Systems Of Typementioning

confidence: 99%

“…Yokoyama [12] classified the types of irreducible rigid Okubo systems under the condition that the nontrivial local exponents are mutually distinct at each finite singular point; this class consists of eight types I, II, III, IV and I Ã , II Ã , III Ã , IV Ã , which is usually referred to as Yokoyama's list. For each type in Yokoyama's list, Haraoka constructed a canonical form of the Okubo system [1], as well as the corresponding monodromy representation, up to the action of diagonal matrices [2]. The purpose of this paper is to propose a method for determining the explicit monodromy representation for Okubo's canonical solution matrix, including the diagonal matrix factor which has not been fixed in [2].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Connection Coefficients and Monodromy Representations for a Class of Okubo Systems of Ordinary Differential Equations

Konnai¹

2018

View full text Add to dashboard Cite

show abstract

“…In the cases of type ðIIÞ 2n and ðIIIÞ 2nþ1 , the following canonical forms of the Okubo systems are proposed by Haraoka [1].…”

Section: Okubo Systems Of Types I Imentioning

confidence: 99%

Section: Construction Of Canonical Forms Of the Okubo Systems Of Typementioning

confidence: 99%

Section: Construction Of Canonical Forms Of the Okubo Systems Of Typementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Connection Coefficients and Monodromy Representations for a Class of Okubo Systems of Ordinary Differential Equations

Konnai¹

2018

View full text Add to dashboard Cite

show abstract

“…On the assumptions (4.34) and (4.36) [28], an irreducible Fuchsian system (4.32) is accessoryfree if [28],…”

Section: Jhep06(2016)137mentioning

confidence: 99%

Correlation functions with fusion-channel multiplicity in W 3 $$ {\mathcal{W}}_3 $$ Toda field theory

Belavin

Estienne

Foda

et al. 2016

J. High Energ. Phys.

View full text Add to dashboard Cite

Current studies of W N Toda field theory focus on correlation functions such that the W N highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W 3 Toda 4-point functions with multiplicity in the fusion channel. The conformal blocks of these 4-point functions involve matrix elements of a fullydegenerate primary field with a highest-weight in the adjoint representation of sl 3 , and a fully-degenerate primary field with a highest-weight in the fundamental representation of sl 3 . We show that, when the fusion rules do not involve multiplicities, the matrix elements of the fully-degenerate adjoint field, between two arbitrary descendant states, can be computed explicitly, on equal footing with the matrix elements of the semi-degenerate fundamental field. Using null-state conditions, we obtain a fourth-order Fuchsian differential equation for the conformal blocks. Using Okubo theory, we show that, due to the presence of multiplicities, this differential equation belongs to a class of Fuchsian equations that is different from those that have appeared so far in W N theories. We solve this equation, compute its monodromy group, and construct the monodromy-invariant correlation functions. This computation shows in detail how the ambiguities that are caused by the presence of multiplicities are fixed by requiring monodromy-invariance.

show abstract

Construction of rigid local systems and integral representations of their sections

Haraoka

Yokoyama

2005

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

We give a method for constructing all rigid local systems of semi-simple type, which is different from the KatzDettweiler-Reiter algorithm. Our method follows from the construction of Fuchsian systems of differential equations with monodromy representations corresponding to such local systems, which give an explicit solution of the Riemann-Hilbert problem. Moreover, we show that every section of such local systems has an integral representation.

show abstract

Canonical Forms of Differential Equations Free from Accessory Parameters

Cited by 17 publications

References 1 publication

Connection Coefficients and Monodromy Representations for a Class of Okubo Systems of Ordinary Differential Equations

Connection Coefficients and Monodromy Representations for a Class of Okubo Systems of Ordinary Differential Equations

Correlation functions with fusion-channel multiplicity in W 3 $$ {\mathcal{W}}_3 $$ Toda field theory

Construction of rigid local systems and integral representations of their sections

Contact Info

Product

Resources

About