Quantum integrable models, algebraic and thermodynamic Bethe ansatz. Representation theory of quantum groups and their applications in theoretical physics.
Biography
Graduated from Physics Department of St. Petersburg State University, chair of mathematical physics — 1993. PhD — 1996.
Main publications:
A. G. Bytsko, V. Schomerus, Vertex operators – from toy model to lattice algebras. Commun. Math. Phys. 191 (1998), 87–136.
A. G. Bytsko, Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities. J. Phys. A 32 (1999), 8045–8058.
A. G. Bytsko, A. Fring, Factorized combinations of Virasoro characters. Commun. Math. Phys. 209 (2000), 179–205.
A. Bytsko, J. Teschner, R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R)). Commun. Math. Phys. 240 (2003), 171–196.
A. G. Bytsko, O Uq(sl_2)-invariantnykh R-matritsakh dlya starshikh spinov. Algebra i analiz, 17 (2005), n. 3, 23–46.
A. G. Bytsko, J. Teschner, Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model. J. Phys. A 39 (2006), 12927–12981.
A. G. Bytsko, “Two relations for the antisymmetrizer in the Hecke algebra”, Zap. Nauchn. Sem. POMI, 509 (2021), 89–98
2012
2.
A. G. Bytsko, I. Yu. Davydenkova, “On quantum $L$-operator for two-dimensional lattice Toda model”, Zap. Nauchn. Sem. POMI, 398 (2012), 87–99; J. Math. Sci. (N. Y.), 192:1 (2013), 50–56
2010
3.
A. G. Bytsko, “Non-Hermitian spin chains with inhomogeneous coupling”, Algebra i Analiz, 22:3 (2010), 80–106; St. Petersburg Math. J., 22:3 (2011), 393–410
A. G. Bytsko, “On constant $U_q(sl_2)$-invariant $R$-matrices”, Zap. Nauchn. Sem. POMI, 374 (2010), 82–91; J. Math. Sci. (N. Y.), 168:6 (2010), 805–810
2007
5.
A. G. Bytsko, I. E. Shenderovich, “On string solutions of Bethe equations in $\mathcal{N}=4$ supersymmetric Yang–Mills theory”, Zap. Nauchn. Sem. POMI, 347 (2007), 75–87; J. Math. Sci. (N. Y.), 151:2 (2008), 2840–2847
2006
6.
A. G. Bytsko, “On one ansatz for $\mathrm{sl}_2$-invariant $R$-matrices”, Zap. Nauchn. Sem. POMI, 335 (2006), 100–118; J. Math. Sci. (N. Y.), 143:1 (2007), 2754–2764
A. G. Bytsko, “On $U_q(sl_2)$-invariant $R$-matrices for senior spins”, Algebra i Analiz, 17:3 (2005), 24–46; St. Petersburg Math. J., 17:3 (2006), 393–408
A. G. Bytsko, “Fusion of $q$-tensor operators: quasi-Hopf-algebraic point of view”, Zap. Nauchn. Sem. POMI, 245 (1997), 107–129; J. Math. Sci. (New York), 100:2 (2000), 2077–2091
1994
10.
A. G. Bytsko, “The zero-curvature representation for nonlinear $O(3)$ sigma-model”, Zap. Nauchn. Sem. POMI, 215 (1994), 100–114; J. Math. Sci. (New York), 85:1 (1997), 1619–1628
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