אודות
Representation theory; semisimple Lie algebras
פרסומים
- STRATIFICATION OF A SINGULAR COMPONENT OF A SPRINGER FIBER OVER x 2 = 0 OF THE SIMPLEST TYPE, Mansour, R. & Melnikov, A., Jun 2023, In: Transformation Groups. 28, 2, p. 867-910 44 p.
- On the existence of smooth orbital varieties in simple Lie algebras, Fresse, L. & Melnikov, A., 1 Jun 2020, In: Journal of the London Mathematical Society. 101, 3, p. 960-983 24 p.
- THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x 2 = 0, Mansour, R. & Melnikov, A., 2020, In: Transformation Groups. 27, 2, p. 597-633 37 p.
- Derjaguin’s Water II: a surface hydration phenomenon, Klugman, I., Melnikov, A. & Parsons, D. F., 2019, In: Substantia. 3, 2, p. 55-58 4 p.
- Representations and Nilpotent Orbits of Lie Algebraic Systems, Gorelik, M. (Editor), Hinich, V. (Editor) & Melnikov, A. (Editor), 2019, Springer. 570 p. (Progress in Mathematics)
- B-ORBITS OF SQUARE ZERO IN NILRADICAL OF THE SYMPLECTIC ALGEBRA, Barnea, N. & Melnikov, A., 1 Dec 2017, In: Transformation Groups. 22, 4, p. 885-910 26 p.
- B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev, Barnea, N. & Melnikov, A., 2016, Lie Theory and Its Applications in Physics. Dobrev, V. (ed.). Springer New York LLC, p. 399-411 13 p. (Springer Proceedings in Mathematics and Statistics; vol. 191).
- On the structure of smooth components of Springer fibers, Fresse, L., Melnikov, A. & Sakas-Obeid, S., 2015, In: Proceedings of the American Mathematical Society. 143, 6, p. 2301-2315 15 p.
- Unimodality of the distribution of Betti numbers for some Springer fibers, Fresse, L., Mansour, R. & Melnikov, A., 1 Oct 2013, In: Journal of Algebra. 391, p. 284-304 21 p.
- B-orbits of nilpotency order 2 and link patterns, Melnikov, A., Mar 2013, In: Indagationes Mathematicae. 24, 2, p. 443-473 31 p.
- Smooth orbital varieties and orbital varieties with a dense B-orbit, Fresse, L. & Melnikov, A., 2013, In: International Mathematics Research Notices. 2013, 5, p. 1122-1203 82 p.
- Highlights in Lie algebraic methods, Joseph, A. (Editor), Melnikov, A. (Editor) & Penkov, I. (Editor), 1 Jan 2012, Birkhauser Boston. 227 p.
- Some characterizations of singular components of springer fibers in the two-column case, Fresse, L. & Melnikov, A., Dec 2011, In: Algebras and Representation Theory. 14, 6, p. 1063-1086 24 p.
- On geometric properties of orbital varieties in type A, Fresse, L. & Melnikov, A., Jul 2011, In: Comptes Rendus Mathematique. 349, 13-14, p. 735-739 5 p.
- On the singularity of the irreducible components of a Springer fiber in sln, Fresse, L. & Melnikov, A., 2010, In: Selecta Mathematica, New Series. 16, 3, p. 393-418 26 p.
- Codimension one intersections of the components of a Springer fiber for the two-column case, Melnikov, A. & Pagnon, N. G. J., Mar 2009, In: Indagationes Mathematicae. 20, 1, p. 101-130 30 p.
- Reducibility of the intersections of components of a Springer fiber, Melnikov, A. & Pagnon, N. G. J., Dec 2008, In: Indagationes Mathematicae. 19, 4, p. 611-631 21 p.
- On orbital variety closures in sln III. Geometric properties, Melnikov, A., 1 Nov 2006, In: Journal of Algebra. 305, 1, p. 68-97 30 p.
- Description of B-orbit closures of order 2 in upper-triangular matrices, Melnikov, A., Jun 2006, In: Transformation Groups. 11, 2, p. 217-247 31 p.
- On intersections of orbital varieties and components of Springer fiber, Melnikov, A. & Pagnon, N. G. J., 1 Apr 2006, In: Journal of Algebra. 298, 1, p. 1-14 14 p.
- On varieties in an orbital variety closure in semisimple Lie algebras, Melnikov, A., 1 Jan 2006, In: Journal of Algebra. 295, 1, p. 44-50 7 p.
- Studies in Lie theory, Bernstein, J. (Editor), Hinich, V. (Editor) & Melnikov, A. (Editor), 2006, Boston: Birkhauser. 490 p. (Progress in Mathematics; vol. 243)
- The combinatorics of orbital varieties closures of nilpotent order 2 in sln, Melnikov, A., 6 May 2005, In: Electronic Journal of Combinatorics. 12, 1 R
- On orbital variety closures in sln II. Descendants of a Richardson orbital variety, Melnikov, A., 15 Jan 2004, In: Journal of Algebra. 271, 2, p. 698-724 27 p.
- On orbital variety closure in sln. I. Induced duflo order, Melnikov, A., 1 Jan 2004, In: Journal of Algebra. 271, 1, p. 179-233 55 p.
- Quantization of Hypersurface Orbital Varieties in sl(n), Joseph, A. & Melnikov, A., 2003, The Orbit Method in Geometry and Physics: In Honor of A.A. Kirillov. Duval, C., Ovsienko, V. & Guieu, L. (eds.). Boston, MA: Birkhauser, p. 165-196 32 p.
- Studies in Memory of Issai Schur, Joseph, A. (Editor), Melnikov, A. (Editor) & Rentschler, R. (Editor), 2002, Boston: Birkhauser. 500 p. (Progress in Mathematics; vol. 210)
- B-Orbits in solutions to the equation X2 = 0 in triangular matrices, Melnikov, A., 1 Jan 2000, In: Journal of Algebra. 223, 1, p. 101-108 8 p.
- Orbital Varieties in slNand the Smith Conjecture, Melnikov, A., 1 Feb 1998, In: Journal of Algebra. 200, 1, p. 1-31 31 p.
- Dense orbits in orbital varieties, Melnikov, A., 1997, Séminaires et Congrès. Alev, J. & Cauchon, G. (eds.). Societe Mathematique de France, Vol. 2. p. 281-294 14 p.
- On a Remarkable Sequence of Polynomials, Kirillov, A. A. & Melnikov, A., 1997, Séminaires et Congrès. Alev, J. & Cauchon, G. (eds.). Societe Mathematique de France, Vol. 2. p. 35-42 8 p.
- Irreducibility of the associated varieties of simple highest weight modules in sl(n), Melnikov, A., Jan 1993, In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 316, 1, p. 53-57 5 p.
- Robinson-Schensted procedure and combinatorial properties of geometric order sl(n), Melnikov, A., Sep 1992, In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 315, 6, p. 709-714 6 p.