Rigged Configurations and Catalan, Stretched Parabolic Kostka Numbers and Polynomials : Polynomiality, Unimodality and Log-concavity
Preprint RIMS-1824, 2015, arXiv:1505.
Construction of double Grothendieck polynomials of classical types using Id-Coxeter algebras (with H. Naruse)
Preprint RIMS-1823, 2015, arXiv:1504.08089.
On Double Schubert and Grothendieck polynomials for Classical Groups
Preprint RIMS-1820, 2015, arXiv:1504.01469.
On some quadratic algebras I+I/2$:
Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck,
Fuss-Catalan, universal Tutte and Reduced polynomials
SIGMA 12(2016) 002, 172 pp.;
Preprint RIMS-1817, 2015, arXiv:1502.00426.
Notes on Schubert, Grothendieck and Key polynomials
Preprint RIMS-1815, 2015, arXiv:1501.07337.
Bethe subalgebras in Hecke algebra and Gaudin models (with A.Isaev) Letters in Mathematical Physics, 104,
(2014) 179-193 Preprint RIMS-1775, 2013
Some Remarks On Nepomechie--Wang Eigenstates For Spin 1/2 XXX Model
(with R. Sakamoto) Moscow Mathematical Journal,
volume 15 , Number 2, April-June 2015, Pages 1-16
Singular Solutions to the Bethe Ansatz Equations and Rigged
Configurations
(with R. Sakamoto)
J. Phys. A: Math. Theor. 47 (2014) 205207 (20pp)
On some combinatorial and algebraic properties of Dunkl elements RIMS Kokyuroku, 1795, 1-44, Kyoto University, 2012
On some algebraic and combinatorial properties of Dunkl elements The Korepin Festschrift, World Scientific (2013), 171-198
On some algebraic and combinatorial properties of Dunkl elements International Journal of Modern Physics B, 26 (2012),
No. 27n28
Affine nil-Hecke algebras and braided differential structure on affine Weyl groups (with T.Maeno) Publ. RIMS, no. 48 (2012), 215-228
Entanglment in valence-bond-solid states on symmetric graphs (with H.Katsura, N.Kawashima, V.Korepin, S.Tanaka)
J. Phys. A43 (2010), no.255303, 28p.
Nichols-Woronowicz model of coinvariant algebra of complex reflection groups (with T.Maeno) J. Pure Appl. Algebra 214 (2010), 402-409
Combinatorics and geometry of higher level Weyl modules Moscow Seminar on Mathematical Physics II,
Amer. Math. Soc. Transl. Ser. 2, 221,
Amer. Math. Soc., Providence, RI, 2007, 33-47
(with Feigin B., Loktev S.)
Preprint RIMS-1495, 2005, 15p. math.QA/0503315
Skew divided difference operators and Schubert polynomials
J. Pure Appl. Algebra
SIGMA3 (2007) 072, 14 pages
Preprint CRM-2526, 1997, 15p.; q-alg/9712053
Wonderful Amoebas (Japanese, with T.Maeno) Sugaku 58 (2006), 151-164, translation in
Sugaku Expositions22 (2009), 107-120
On some noncommutative algebras related with K-theory of flag
varieties, I (with T.Maeno)
IRMN60 (2005), 3753-3789
Preprint RIMS, 2005, 25p. math.CO/0504290
A note on quantization on Nichols algebra model for Schubert
calculus on Weyl groups (with T.Maeno)
Lett. in Math. Phys.72 (2005) 233-241
Preprint RIMS-1481, 2004, 8p. math.QA/0412069
Hypergeometric generating function of L-function, Slater's
identities and Quantum invariant (with K.Hikami)
Algebra i Analiz17 (2005), no.1, 190-208
Preprint RIMS-1463, 2004, 18p. math-ph/0406042
New combinatorial formula for modified Hall-Littlewood polynomials q-Series from a Contemporary Perspective (AMS-ISM-SIAM Joint
Summer Research Conference on q-series, Combinatorics, and computer
Algebra; June 21-25, 1998, Mount Holyoke, MA, USA), 283-333, Contemporary Mathematics254, AMS, Providence, RI, 2000
math.QA/9803006
On some quadratic algebras: Jucys-Marphy and Dunkl elements
Calogero-Moser-Sutherland models,
(Montreal, PQ, March 10-15, 1997) CRM Series in Mathematical Physics,
Springer, New York, 2000, 231-248
Formulae for the multiplicites of the occurrence of irreducible
components in the tensor product of representations of simple Lie
algebras (Russian, with
N.Yu.Reshetikhin)
Zap. Nauch. Sem. LOMI205 (1993), 30-37, translation in
Journal of Mathematical Sciences80, no.3 (1996),
1768-1772
On some properties of the Robinson-Schensted correspondence Proceedings of Hayashibara conference on special functions,
1990, 122-126.
Representation of quantum groups, combinatorics, q-orthogonal
polynomials and link invariants
(Russian) Second Ph.D thesises, LOMI, Leningrad, 1990, 300p.
On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan
numbers
Journ. Geom. and Phys.5 (1988), 365-389.
Multiplicity of weight in irreducible tensor representations of
a complete linear syperalgebra (Russian, with
N.Yu.Reshetikhin)
Funct. Anal. and Applicat.22 (1988), no.4, 84-85.
Identities for the Rogers dilogarithmic function connected with
simple Lie algebras
(Russian)
Zap. Nauch. Sem. LOMI164 (1987), 121-133,
translation in
Journal of Soviet Math.47 (1989), 2450-2458.
Solution of some combinatorial problems arising in the calculation
of correlators in exactly solvable models
(Russian, with
F.A.Smirnov)
Zap. Nauch. Sem. LOMI164 (1987), 67-79,
translation in
Journal of Soviet Math.47 (1989), 2413-2422.
A representation of the current algebra connected with
SU(2)-invariant Thirring model
(with
F.A.Smirnov)
Phys. Lett. B198 (1987), no.4, 506-510.
The Bethe ansatz and the combinatorics of Young tableaux
(Russian) Ph.D thesises, LOMI, Leningrad, 1987, 210p.
Exact solution of the integrable XXZ Heisenberg model with
arbitrary spin, I (with
N.Yu.Reshetikhin)
J. Phys. A20 (1987), 1565-1586.
Exact solution of the integrable XXZ Heisenberg model with
arbitrary spin, II (with
N.Yu.Reshetikhin)
J. Phys. A20 (1987), 1587-1597.
Quantum inhomogeneous XXZ magnet and non-linear
$\sigma$-models (with
N.Yu.Reshetikhin) Proceedings of Paris-Meudon Colloquium, Paris, 1987,
235-257.
Representation of Yangians and multiplicities of the inclusion
of the irreducible components of the tensor product of representations
of simple Lie algebras (Russian, with
N.Yu.Reshetikhin)
Zap. Nauch. Sem. LOMI160 (1987), 211-221,
translation in
Journal of Soviet Math.52 (1990), 3156-3164.
Some generalization of the Abjankar-Moh theorem
(Russisn) Proceedings of Algebraic Conference, L'vov, 1987, part 1,
p.131.
T-invariance, CPT-invariants and local commutativity
of the quantum $(ch\varphi)_2$ model
(Russian)
Zap. Nauch. Sem. LOMI146 (1985), 9-19,
translation in
Journal of Soviet Math.40 (1988), 6-12.
Combinatorial identities and completeness of states for the
Heisenberg magnet
(Russian)
Zap. Nauch. Sem. LOMI131 (1983), 88-105,
translation in
Journal of Soviet Math.30 (1985), 2298-3310.
Mixed Hodge structure of the isolated singularity of the
hypersuface Shot Communications, ICM-82, Warszawa, 1982, sec.6, p.34.
Milnor's number of isolated singularity of complete intersection
(Russian) Proceedings of Algebraic conference, Leningrad, 1981,
part 1, p.97.
The Zeta function of the monodromy of a singular point of complete
intersection
(Russian)
Zap. Nauch. Sem. LOMI112 (1981), 112-119,
translation in
Journal of Soviet Math.25 (1984), 1051-1056.
Formula for calculating the integer cohomology of the link of
an isolated hypersurface singularity
(Russian)
Zap. Nauch. Sem. LOMI100 (1980), 106-112,
translation in
Journal of Soviet Math.19 (1982), 1695-1699.