AK
Anatol Kirillov
math.QAhep-thmath.COq-algmath.MPmath-phmath.CAmath.ACmath.RTcond-mat.stat-mech
On Valency
published · living versionsW_wxq8qcu2·v1 · currentpublished
W_ejs5vcck·v1published
Preprints & journals
53 papers in the corpus · 1992–2026Elementary Askey-Wilson Functions2609.37390v1 · J.F. van Diejen, A.N. Kirillov2026 · 0 citationsarXiv
Matching algebras and their Dunkl subalgebras2609.34260v2 · Darij Grinberg, Anatol Kirillov, Boris Shapiro2026 · 0 citationsarXivon Valency
The Loopy Polynomial: from Tutte's Universal -Function to Bizonotopal Geometry2609.07728v2 · Anatol Kirillov, Gleb Nenashev, Boris Shapiro et al.2026 · 0 citationsarXiv
A Matrix Model for Higher-Genus Fuss--Catalan Numbers2605.24237v3 · Anatol Kirillov, Ivan Kostov2026 · 0 citationsarXiv
Bizonotopal Graphical Algebras2407.19431v2 · Anatol Kirillov, Gleb Nenashev, Boris Shapiro et al.2024 · 0 citationsarXiv
Hook-content formula using excited Young diagrams1904.00371v1 · Anatol N. Kirillov, Travis Scrimshaw2019 · 1 citationarXiv
On -deformations of Postnikov-Shapiro algebras1708.06815v1 · Anatol N. Kirillov, Gleb Nenashev2017 · 1 citationarXiv
Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations1510.05374v2 · A.P. Isaev, A.N. Kirillov, V.O. Tarasov2015 · 4 citationsarXiv
Bethe's Quantum Numbers And Rigged Configurations1509.02305v3 · Anatol N. Kirillov, Reiho Sakamoto2015 · 1 citationNuclear Physics B 905 (2016) 359-372
Construction of double Grothendieck polynomials of classical types using IdCoxeter algebras1504.08089v2 · A.N. Kirillov, H. Naruse2015 · 16 citationsTokyo J. Math.Volume 39, Number 3 (2017), 695-728
On Some Quadratic Algebras I : Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials1502.00426v3 · Anatol N. Kirillov2015 · 18 citationsSIGMA 12 (2016), 002
Notes on Schubert, Grothendieck and Key Polynomials1501.07337v3 · Anatol N. Kirillov2015 · 22 citationsSIGMA 12 (2016), 034, 57 pages
Some Remarks On Nepomechie--Wang Eigenstates For Spin 1/2 XXX Model1406.1958v4 · Anatol N. Kirillov, Reiho Sakamoto2014 · 6 citationsMoscow Mathematical Journal 15 (2015) 337--352
Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations1402.0651v2 · Anatol N. Kirillov, Reiho Sakamoto2014 · 24 citationsJ. Phys. A: Math. Theor. 47 (2014) 205207 (20pp)
Bethe subalgebras in Hecke algebra and Gaudin models1302.6495v1 · A. P. Isaev, Anatol N. Kirillov2013 · 11 citationsarXiv
Affine nil-Hecke algebras and braided differential structure on affine Weyl groups1008.3593v1 · Anatol N. Kirillov, Toshiaki Maeno2010 · 3 citationsarXiv
Entanglement in valence-bond-solid states on symmetric graphs1003.2007v2 · Hosho Katsura, Naoki Kawashima, Anatol N. Kirillov et al.2010 · 25 citationsJ. Phys. A: Math. Theor. 43 (2010) 255303
Generalized Energy Statistics and Kostka--Macdonald Polynomials0912.2161v2 · Anatol N. Kirillov, Reiho Sakamoto2009 · 0 citationsDMTCS proc. AN (2010) 343--354
The valence bond solid in quasicrystals0909.2211v1 · Anatol N. Kirillov, Vladimir E. Korepin2009 · 5 citationsALGEBRA and ANALYSIS, vol 1, issue 2, page 47, 1989 [in Russian language]
Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations0902.2286v2 · Anatol N. Kirillov, Reiho Sakamoto2009 · 9 citationsLetters in Mathematical Physics 89 (2009) 51-65
Paths and Kostka--Macdonald Polynomials0811.1085v2 · Anatol N. Kirillov, Reiho Sakamoto2008 · 2 citationsMoscow Mathematical Journal 9 (2009) 823--854
Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties0712.2580v3 · Anatol N. Kirillov, Toshiaki Maeno2007 · 4 citationsarXiv
Braided differential structure on Weyl groups, quadratic algebras and elliptic functions0709.4599v2 · Anatol N. Kirillov, Toshiaki Maeno2007 · 2 citationsarXiv
Skew Divided Difference Operators and Schubert Polynomials0705.4546v1 · Anatol N. Kirillov2007 · 9 citationsSIGMA 3 (2007), 072, 14 pages
Nichols-Woronowicz model of coinvariant algebra of complex reflection groupsmath/0703748v1 · Anatol N. Kirillov, Toshiaki Maeno2007 · 6 citationsarXiv
Combinatorics and Geometry of Higher Level Weyl Modulesmath/0503315v3 · B. Feigin, A.N. Kirillov, S. Loktev2005 · 21 citationsAMS Transl., Ser. 2, 221 (2007)
A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groupsmath/0412069v4 · Anatol. N. Kirillov, Toshiaki Maeno2004 · 8 citationsarXiv
Torus Knot and Minimal Modelhep-th/0308152v1 · Kazuhiro Hikami, Anatol N. Kirillov2003 · 38 citationsPhys.Lett. B575 (2003) 343-348
Bethe's states for generalized XXX and XXZ modelsmath/0103030v1 · Anatol N. Kirillov, Nadejda Liskova2001 · 1 citationarXiv
Character Formulae of -Modules and Inhomogeneous Pathsmath/9802085v2 · Goro Hatayama, Anatol N. Kirillov, Atsuo Kuniba et al.1998 · 57 citationsNuclear Physics B 536 [PM] (1999), 575-616
Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levelsq-alg/9711009v1 · Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi1997 · 3 citationsNucl. Phys. B529 [PM] (1998) 611-638
Domino tableaux, Schutzenberger involution, and the symmetric group actionq-alg/9709010v2 · Arkady Berenstein, Anatol N. Kirillov1997 · 4 citationsarXiv
On some quadratic algebrasq-alg/9705003v3 · Anatol N. Kirillov1997 · 0 citationsarXiv
Cauchy identities for universal Schubert polynomialsq-alg/9703047v1 · Anatol N. Kirillov1997 · 6 citationsarXiv
Quantum Schubert polynomials and quantum Schur functionsq-alg/9701005v3 · Anatol N. Kirillov1997 · 6 citationsarXiv
Quantum Grothendieck polynomialsq-alg/9610034v1 · Anatol N. Kirillov1996 · 5 citationsarXiv
Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formulaq-alg/9610022v3 · Anatol N. Kirillov, Toshiaki Maeno1996 · 36 citationsarXiv
Skew Young diagram method in spectral decomposition of integrable lattice modelsq-alg/9607027v1 · Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi1996 · 38 citationsCommun.Math.Phys. 185 (1997) 441-465
Affine Hecke algebras and raising operators for Macdonald polynomialsq-alg/9605004v1 · Anatol N. Kirillov, Masatoshi Noumi1996 · 84 citationsarXiv
-Difference raising operators for Macdonald polynomials and the integrality of transition coefficientsq-alg/9605005v1 · Anatol N. Kirillov, Masatoshi Noumi1996 · 11 citationsarXiv
Dilogarithm identitieshep-th/9408113v2 · Anatol N. Kirillov1994 · 255 citationsProg.Theor.Phys.Suppl.118:61-142,1995on Valency
Completeness of Bethe's states for generalized modelhep-th/9403107v2 · Anatol N. Kirillov, Nadejda A. Liskova1994 · 35 citationsJ.Phys.A30:1209-1226,1997
Universal exponential solution of the Yang-Baxter equationhep-th/9306093v1 · Sergey Fomin, Anatol N. Kirillov1993 · 16 citationsLett.Math.Phys. 37 (1996) 273-284
Combinatorial -analogues of Schubert polynomialshep-th/9306053v1 · Sergey Fomin, Anatol N. Kirillov1993 · 20 citationsarXiv
Yang-Baxter equation, symmetric functions and Grothendieck polynomialshep-th/9306005v2 · Sergey Fomin, Anatol N. Kirillov1993 · 17 citationsarXiv
Generalization of the Gale-Ryser theoremhep-th/9304099v2 · Anatol N. Kirillov1993 · 2 citationsarXiv
Berenstein-Zelevinsky triangles, elementary couplings and fusion ruleshep-th/9301075v1 · L. Begin, Anatol N. Kirillov, P. Mathieu et al.1993 · 30 citationsLett.Math.Phys. 28 (1993) 257-268
Unimodality of generalized Gaussian coefficientshep-th/9212152v1 · Anatol N. Kirillov1992 · 7 citationsarXiv
Dilogarithm identities, partitions and spectra in conformal field theory, Ihep-th/9212150v1 · Anatol N. Kirillov1992 · 0 citationsarXiv
Fusion algebra and Verlinde's formulahep-th/9212084v1 · Anatol N. Kirillov1992 · 2 citationsarXiv
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