Derkachov Sergei Èduardovich

Publications in Math-Net.Ru

1. A-Type Open ${\rm SL}(2,\mathbb{C})$ Spin Chain
   
   SIGMA, 21 (2025), 107, 48 pp.
2. Factorization of the $\mathfrak{sl}(2|1)$ invariant R-matrix
   
   Zap. Nauchn. Sem. POMI, 548 (2025),  70–100
3. Reflection operator and hypergeometry II: $SL(2,\mathbb{C})$ spin chain
   
   Zap. Nauchn. Sem. POMI, 532 (2024),  47–79
4. Reflection operator and hypergeometry I: $SL(2,\mathbb{R})$ spin chain
   
   Zap. Nauchn. Sem. POMI, 532 (2024),  5–46
5. Baxter $Q$-operators in Ruijsenaars–Sutherland hyperbolic systems: one- and two-particle cases
   
   Zap. Nauchn. Sem. POMI, 520 (2023),  50–123
6. Elliptic hypergeometric function and $6j$-symbols for the $SL(2,\pmb{\mathbb C})$ group
   
   TMF, 213:1 (2022),  108–128
7. Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains
   
   SIGMA, 17 (2021), 063, 26 pp.
8. Racah coefficients for the group $\mathrm{SL}(2,\mathbb{R})$
   
   Zap. Nauchn. Sem. POMI, 509 (2021),  99–112
9. On Complex Gamma-Function Integrals
   
   SIGMA, 16 (2020), 003, 20 pp.
10. Mellin–Barnes transformation for two-loop master-diagrams
    
    Zap. Nauchn. Sem. POMI, 494 (2020),  144–167
11. Regular representation of the group $\mathrm{GL}(N,\mathbb{R})$: factorization, Casimir operators and Toda chain
    
    Zap. Nauchn. Sem. POMI, 494 (2020),  23–47
12. The $6j$-symbols for the $SL(2,\mathbb C)$ group
    
    TMF, 198:1 (2019),  32–53
13. Completeness of the $3j$-symbols for $SL(2,\mathbb C)$ group
    
    Zap. Nauchn. Sem. POMI, 487 (2019),  40–52
14. $\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals
    
    SIGMA, 14 (2018), 030, 16 pp.
15. Separation of variables for the quantum $SL(3,\mathbb{C})$ spin magnet: eigenfunctions of Sklyanin $B$-operator
    
    Zap. Nauchn. Sem. POMI, 473 (2018),  110–146
16. $Q$-operator for the quantum NLS model
    
    Zap. Nauchn. Sem. POMI, 473 (2018),  34–65
17. Renormalization scenario for the quantum Yang–Mills theory in four-dimensional space–time
    
    TMF, 192:2 (2017),  227–234
18. Remark on the reflection coefficient in the Liouville model
    
    TMF, 192:2 (2017),  221–226
19. Orthogonal polynomials, $6j$-symbols and statistical weights of SOS models
    
    Zap. Nauchn. Sem. POMI, 465 (2017),  105–134
20. SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams
    
    Zap. Nauchn. Sem. POMI, 465 (2017),  82–104
21. From Principal Series to Finite-Dimensional Solutions of the Yang–Baxter Equation
    
    SIGMA, 12 (2016), 028, 34 pp.
22. Construction of eigenfunctions for a system of quantum minors of the monodromy matrix for an $SL(n,\mathbb C)$-invariant spin chain
    
    TMF, 189:2 (2016),  149–175
23. Finite-dimensional representations of the elliptic modular double
    
    TMF, 183:2 (2015),  177–201
24. Matrix factorization for solutions of the Yang–Baxter equation
    
    Zap. Nauchn. Sem. POMI, 433 (2015),  156–185
25. Yang–Baxter equation, parameter permutations, and the elliptic beta integral
    
    Uspekhi Mat. Nauk, 68:6(414) (2013),  59–106
26. The $R$-matrix factorization, $Q$-operator, and variable separation in the case of the $XXX$ spin chain with the $SL(2,\mathbb{C})$ symmetry group
    
    TMF, 169:2 (2011),  204–217
27. On rational symplectic parametrization of the coadjoint orbit of $\mathrm{GL}(N)$. Diagonalizable case
    
    Algebra i Analiz, 22:3 (2010),  16–31
28. Green function in the quantum Coulomb problem
    
    Zap. Nauchn. Sem. POMI, 374 (2010),  170–196
29. On the spectrum of anomalous dimensions of composite operators in the scalar field theory
    
    Zap. Nauchn. Sem. POMI, 374 (2010),  136–169
30. General solution of the Yung–Baxter equation with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$
    
    Algebra i Analiz, 21:4 (2009),  1–94
31. Factorization of the R-matrix and Baxter's Q-operator
    
    Zap. Nauchn. Sem. POMI, 347 (2007),  144–166
32. Factorization of the $\mathcal R$-matrix for the algebra $U_q(s\ell_3)$
    
    Zap. Nauchn. Sem. POMI, 347 (2007),  88–106
33. $\mathcal R$-Matrix and Baxter $\mathcal Q$-Operators for the Noncompact $\mathrm{SL}(N,\mathbb C)$ Invariant Spin Chain
    
    SIGMA, 2 (2006), 084, 20 pp.
34. Factorization of the R-matrix. II
    
    Zap. Nauchn. Sem. POMI, 335 (2006),  164–187
35. Factorization of the $\mathrm{R}$-matrix. I
    
    Zap. Nauchn. Sem. POMI, 335 (2006),  134–163
36. Critical dimensions of composite operators in the nonlinear $\sigma$-model
    
    TMF, 116:3 (1998),  379–400
37. Three loops calculation of the field anomalous dimension in the full four-fermion $U_N$-symmetrical model
    
    TMF, 107:3 (1996),  359–371
38. On equivalence of renormalizations for standard and dimensional regularizations of $2D$ four-fermion interactions
    
    TMF, 107:1 (1996),  27–46
39. A technique for calculating the $\gamma$-matrix structures of the diagrams of a total four-fermion interaction with infinite number of vertices $d=2+\epsilon$ dimensional regularization
    
    TMF, 103:2 (1995),  179–191
40. The $1/n$ expansion in the Gross–Neveu model: Conformal bootstrap calculation of the index $\eta$ in order $1/n^3$
    
    TMF, 94:2 (1993),  179–192
41. Proof of conformal invariance in the critical regime for models of Gross–Neveu type
    
    TMF, 92:3 (1992),  486–497