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INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 06/2018, Volume 2018, Issue 12, pp. 3621 - 3670
Let G be a simply connected simple algebraic group over C, B and B- its two opposite Borel subgroups, and W the associated Weyl group. It is shown that the... 
Q-ANALOG | MATHEMATICS | BASES
Journal Article
QUARTERLY JOURNAL OF MATHEMATICS, ISSN 0033-5606, 09/2019, Volume 70, Issue 3, pp. 895 - 925
The quantum co-ordinate algebra A(q) (g) associated to a Kac-Moody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite-dimensional... 
Q-ANALOG | MATHEMATICS | BASES
Journal Article
Representation Theory of the American Mathematical Society, ISSN 1088-4165, 09/2017, Volume 21, Issue 11, pp. 247 - 276
We reformulate the Kazhdan-Lusztig theory for the BGG category \mathcal {O} of Lie algebras of type D via the theory of canonical bases arising from quantum... 
Q-ANALOG | MATHEMATICS | ALGEBRAS
Journal Article
by Oh, YT and Park, E
ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 11/2019, Volume 26, Issue 4
In this paper, we study a new cyclic sieving phenomenon on the set SSTn(lambda) of semistandard Young tableaux with the cyclic action c arising from its... 
Q-ANALOG | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 10/2019, Volume 15, Issue 9, pp. 1919 - 1968
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding q -supercongruence. Similar q -supercongruences are established... 
q -analogue | Apéry numbers | supercongruence | Gauss congruence | cyclic sieving phenomenon | MATHEMATICS | q-analogue | SERIES | Q-ANALOGS | Apery numbers | FERMAT | FIBONACCI NUMBERS
Journal Article
by Du, J and Fu, Q
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 10/2019, Volume 2019, Issue 20, pp. 6179 - 6215
We will construct the Lusztig form for the quantum loop algebra of gl(n) by proving the conjecture [4, 3.8.6] and establish partially the Schur-Weyl duality at... 
Q-ANALOG | MATHEMATICS | CRYSTAL BASES | CANONICAL BASES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 346, pp. 329 - 358
By examining asymptotic behavior of certain infinite basic (q-) hypergeometric sums at roots of unity (that is, at a ‘q-microscopic’ level) we prove polynomial... 
q-analogue | Cyclotomic polynomial | Basic hypergeometric function | Radial asymptotics | (Super)congruence | WZ pair | Q-ANALOG | MATHEMATICS | CONJECTURES | FORMULAS
Journal Article
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2016, Volume 308, pp. 318 - 329
Journal Article
Journal of Combinatorial Designs, ISSN 1063-8539, 11/2015, Volume 23, Issue 11, pp. 463 - 480
Intersection numbers for subspace designs are introduced and q‐analogs of the Mendelsohn and Köhler equations are given. As an application, we are able to... 
block design | subspace design | q‐analog | Fano plane | intersection number | q-analog | MATHEMATICS | Q-ANALOGS | 2-DESIGNS | T-DESIGNS | Mathematics - Combinatorics
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, pp. 1 - 12
AbstractWe prove some congruences on sums involving fourth powers of centralq-binomial coefficients. As a conclusion, we confirm the following supercongruence... 
cyclotomic polynomials | q-analogue of Wolstenholme's binomial congruence | q-binomial coefficients | q-analogue of Morley's congruence | q-WZ method
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 11/2014, Volume 2014, Issue 5, pp. 1312 - 1366
We give an explicit construction of irreducible modules over Khovanov-Lauda-Rouquier algebras R and their cyclotomic quotients R-lambda for finite classical... 
Q-ANALOG | MATHEMATICS | CRYSTAL BASES
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 8/2014, Volume 72, Issue 2, pp. 405 - 421
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2019, Volume 475, Issue 2, pp. 1636 - 1646
There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work,... 
Cyclotomic polynomial | Basic hypergeometric function | Ramanujan | (Super)congruence | q-Analogue | Q-ANALOG | 1/PI | MATHEMATICS | MATHEMATICS, APPLIED | RAMANUJAN-TYPE FORMULAS | SUPERCONGRUENCE | CONGRUENCES
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 05/2019, Volume 65, Issue 5, pp. 2648 - 2660
Journal Article
Journal Article
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