Stein manifolds and multiplicity-free representations of compact Lie groups, Contemporary Math., Amer. Math. Society, vol. 554 (2011), 1 - 12

Weakly symmetric homogeneous spaces and spherical Stein manifolds, Proceedings of the International Mathematical Conference "50 Years of IITP", July 2011, Moscow

Estimation of multivariate observation-error statistics for AMSU-A data, to appear in Monthly Weather Review

Block characters of the symmetric groups, submitted. arXiv:1108.5044

Markov processes of infinitely many nonintersecting random walks, submitted. arXiv:1106.1299

A pattern theorem for random sorting networks, submitted. arXiv:1110.0160

Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram, J. Algebra, 344 (2011), 197-204.
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Schubert calculus and Gelfand-Zetlin polytopes. arXiv:1101.0278v1 [math.AG], 01/2011. -31 p.
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Fredman’s reciprocity, invariants of abelian groups, and the permanent of the Cayley table, J. Algebraic Combin., 33 (2011), 111-125.
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Mixed Artin-Tate motives with finite coefficients. Moscow Math. Journal 11 (2011), #2, p.317-402.
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Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence. Memoirs of the Amer. Math. Soc. 212 (2011), #996, vi+133 pp.
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Schubert calculus for algebaric cobordism, Journal fuer die reine und angewandte Mathematik (Crelle), DOI: 10.1515/CRELLE.2011.043
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Ilya Shapirovsky: Simulation of Two Dimensions in Unimodal Logics. Advances in Modal Logic 2010: 371-391
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The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices, Advances in Mathematics, 229 (2012), no. 1, 201-266. arXiv:1011.1769

Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group, Funct. Anal. Appl., 44 (2010), no. 2, 92-105. arXiv: 0805.2660

q-Distributions on plane partitions, Selecta Mathematica, New Series, 16 (2010), no. 4, 731-789. arXiv:0905.0679

"Problem of combinatorial computation of rational Pontryagin classes". Doctor of science thesis (profound scientific research work required for attaining higher academic positions or professorships in the former Soviet Union). Summary (34 pages, in Russian). To be defended in Steklov Mathematical Institute on 23 December 2010.
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"Problem of combinatorial computation of rational Pontryagin classes". Doctor of science thesis (profound scientific research work required for attaining higher academic positions or professorships in the former Soviet Union). Full text (341 pages, in Russian). To be defended in Steklov Mathematical Institute (Moscow) on 23 December 2010.
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"Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class", Proc. Stekl. Inst. Math., 268 (2010), 70-86
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q-Exchangeability via quasi-invariance, Annals of Probability 38 (2010), Number 6, 2103-2135; arXiv:0907.3275.
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Plancherel averages: Remarks on a paper by Stanley, Electronic Journal of Combinatorics 17 (2010), paper #R43; arXiv:0905.1304.
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The work of Vladimir Morozov on Lie algebras, Transformation Groups, 15 (2010), 1001-1013.
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On divisible weighted Dynkin diagrams and reachable elements, Transformation Groups, 15 (2010), 983-999.
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Pfaffian Stochastic Dynamics of Strict Partitions, 2010, arXiv:1011.3329.
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Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles, Selecta Math. (New Ser)., 16 (2010), 315–342.
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Random strict partitions and determinantal point processes, Electronic Communications in Probability, 15 (2010), 162-175, arXiv:1002.2714.
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Actions of the derived group of a maximal unipotent subgroup on $G$-varieties, Intern. Math. Res. Notices 2010, no. 4 (2010), 674-700.

Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures. Appendix C in collaboration with D.Rumynin; Appendix D in collaboration with S.Arkhipov. Monografie Matematyczne, vol.70, Birkhäuser/Springer Basel, 2010. xxiv+349 pp.
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On semi-infinite cohomology of finite-dimensional graded algebras. Compositio Math. 146 (2010), #2, p.480-496.
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Gelfand-Zetlin polytopes and flag varieties, International Mathematics Research Notices, vol. 2010. no. 13. pp. 2512—2531
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Shuffling algorithm for boxed plane partitions, Advances in Mathematics, 220 (2009), no. 6. 1739-1770. arXiv: 0804.3071

"A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices", Proc. Stekl. Math. Inst. 266:1 (2009), 29-48
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