Интегрируемые структуры аффинного Янгиана Вильковиский Илья

Короткий опис

Вильковиский, Илья.
Интегрируемые структуры аффинного Янгиана = Integrable structures of the affine Yangian : Integrable structures of the affine Yangian : диссертация ... кандидата физико-математических наук : 01.01.03 / Ilya Vilkoviskiy; [Место защиты: ФГАОУ ВО «Национальный исследовательский университет «Высшая школа экономики»]. - Москва, 2022. - 112 с. : ил.
Оглавление диссертациикандидат наук Вильковиский Илья
Contents
Introduction
0.1 Integrable field theories, integrable structures of CFT
0.2 Thesis results
0.3 Thesis review
1 Affine Yangian and Bethe ansatz
1.1 Introduction
1.2 Maulik-Okounkov R-matrix as Liouville reflection operator
1.3 Yang-Baxter algebra
1.3.1 Current realisation of the Yang-Baxter algebra YB(g[(1))
1.3.2 Center of YB(gl(1))
1.3.3 Zero twist integrable system
1.4 ILW Integrals of Motion and Bethe ansatz
1.4.1 Off-shell Bethe vector
1.4.2 Diagonalization of KZ Integral
1.4.3 Quantum KZ equation
1.4.4 Diagonalization of I2 Integral
1.4.5 Okounkov-Pandharipande equation
1.4.6 Difference equations and norms of Bethe eigenvectors
1.5 Concluding remarks
2 BCD integrable structures and boundary Bethe ansatz
2.1 Introduction
2.2 Integrable systems of BCD type in CFT
2.3 Maulik-Okounkov R-matrix, K-matrix
2.3.1 KZ integrals of motion
2.3.2 Review of the RLL algebra YB(flli)
2.3.3 Antipode
2.4 Off-shell Bethe vector
2.4.1 K operators
2.4.2 Off-shell Bethe vector
2.4.3 Bethe Ansatz equations, eigenvalues of KZ IOMs
2.5 Diagonalization of KZ integral
2.5.1 Strange module
2.5.2 Calculation of K-operator
2.5.3 Off-shell Bethe function, diagonalization of KZ integral
2.6 Concluding remarks
3 Integrals of motion for the deformed W algebras
3.1 Introduction
3.2 Basic Definitions
3.2.1 Higher W currents
3.2.2 Example of WN algebra
3.3 Commutant of affine set of screenings
3.3.1 Example of g[(2)
3.3.2 Example of ¿[(4) = so(6)
3.4 Integrals of Motion of so(2N) type
3.4.1 Integrals of motion for the q-deformed W algebras of BCD type
3.5 R - matrix, K-matrix, and associated KZ Integrals of Motion
3.6 Discussion
Conclusion
Bibliography
Appendix A
A.1 Large u expansion of the operator R(u)
A.2 Affine Yangian commutation relations
A.3 Special vector |x) and shuffle functions
A.4 Other representations of YB(g[(1))
Appendix B
B.1 Restoring the symmetry between ea
Appendix C
C.1 Sklyanin's K matrices