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Photo: Tidal Basin, Washington DC

Last Update: February 1st, 2023

Research Publications:

Publications:

Year
Title / Journal
arXiv Links
2021 On tensor products decomposition of positive representations of Uqq'(sl(2,R)),
Letters in Mathematical Physics, 111(39), (2021)
arXiv Link
2020 Positive representations of split real simply-laced quantum groups,
Publications of the Research Institute of Mathematical Science, 56(3), 603-646, (2020)
arXiv Link
2019 Cluster Realization of positive representations of split real quantum Borel subalgebra,
Theoretical and Mathematical Physics, 198(2), 246-272, (2019)
arXiv Link
2019 (with R. Penner, A. Zeitlin)
On Ramond Decorations
,
Communications in Mathematical Physics, 371, 145-157 (2019)
arXiv Link
2018 (with R. Penner, A. Zeitlin)
N=2
super-Teichmüller theory,
Advances in Mathematics, 336(1), 409-454, (2018)
arXiv Link
2018 Cluster realization of Uq(g) and factorization of universal R-matrix,
Selecta Mathematica New Series, 24(5), 4461-4553,(2018)
arXiv Link
2018 On tensor products of positive representations of split real quantum Borel subalgebra Uqq'(bR),
Transactions of the American Mathematical Society, Vol 370 (6), 4177-4200, (2018)
arXiv Link
2016 Positive Casimir and central characters of split real quantum groups, Communication in Mathematical Physics, Vol 344 (3), 857-888, (2016) arXiv Link
2015
Gauss-Lusztig decomposition of GLq+(N,R) and representations by q-tori,
Journal of Pure and Applied Algebra, Vol 219 (12), 5650-5672, (2015)
arXiv Link
2015
(with M. Yamazaki) Quantum dilogarithm identities at root of unity,
International Mathematics Research Notices, 2016 (3), 669-695, (2015)
arXiv Link
2015 Positive representations of split real quantum groups: the universal R Operator,
International Mathematics Research Notices, Vol 2015 (1), 240-287, (2015)
arXiv Link
2015
Positive representations of non-simply-laced split real quantum groups,
Journal of Algebra, Vol 425, 245-276, (2015)
arXiv Link
2014
(with A. Zeitlin)
Q-operator and fusion relations for Cq(2)(2)
Letters in Mathematical Physics, Vol 104 (8), 1019-1043, (2014)
arXiv Link
2014
(with A. Zeitlin)
Supersymmetry and the modular double
Contemporary Mathematics, Vol 623, 81-97, (2014)
arXiv Link
2014
(with I. Frenkel)
Positive representation of split real quantum groups and future perspectives,
International Mathematics Research Notices, Vol 2014 (8), 2126-2164, (2014)
arXiv Link
2013 The classical limit of representation theory of the quantum plane,
International Journal of Mathematics, Vol 24, No. 4, 1350031 (2013)
arXiv Link
2013
Representation of the quantum plane, its quantum double and harmonic analysis on GLq+(2,R),
Selecta Mathematica New Series, Vol 19 (4), 987-1082, (2013)
arXiv Link

Preprints:

Year
Title
arXiv Links
2023 (with Ryuichi Man)
Casimirs of Parabolic Positive Representations
(in preparation)
2023 (with Jeff York Ye)
On the polynomiality conjecture of cluster realization of quantum groups
arXiv:2302.04020
2022 Quantum cluster mutations and reduced word graphs
arXiv:2211.09601
2022 (with Ryuichi Man)
Positive Representations with Zero Casimirs

arXiv:2203.14828
2020 Parabolic positive representations of Uq(gR)
arXiv:2008.08589
2020 (with G. Schrader, A. Shapiro)
Positive Peter-Weyl theorem
(in preparation)
2011
Graphs of quantum dilogarithm arXiv:1108.5376

Conference Proceedings

2021 Overview of the parabolic positive representations of Uq(gR) ,
Proceedings of 2020 RIMS Conference ``Recent advances in combinatorial representation theory'', (2021)
--
2021 On the parabolic positive representations of split real quantum groups,
Proceedings of ``Symposium on Representation Theory 2020'', (2021)
--
2019 Positive representations: recent developments,
Proceeding of ICCM 2018, (2019)
--
2017 Positive representations, multiplier Hopf algebra, and continuous canonical basis,
Proceedings of 2013 RIMS Conference "String theory, integrable systems and representation theory", Kôkyûroku Bessatsu B62, (2017)
arXiv Link
2012
Igor Frenkel’s contributions to the representation theory of split real quantum groups and modular doubles, "On the work of Igor Frenkel",
Perspectives in Representation Theory, A Conference in Honor of Igor Frenkel's 60th Birthday, Contemporary Mathematics Vol 610, 1-21, ISBN 978-0-8218-9170-4
--
2012
Positive representation of split real quantum groups,
“Symmetries and Groups in Contemporary Physics”,
Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics,
World Scientific Company Vol. 11, “Nankai Series in Pure, Applied Mathematics and Theoretical Physics”; ISBN 978-981-4518-54-3.

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Ph. D. Dissertation:

2012
Positive Representation and Harmonic Analysis of Split Real Quantum Groups
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