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Research
Publications:
Publications:
Year
|
Title
/
Journal
|
arXiv
Links
|
| 2024 |
(with Jeff York Ye)
On the polynomiality conjecture of cluster realization of
quantum groups, Journal of Algebra (to appear, 2024) |
arXiv
Link
|
| 2024 |
(with Ryuichi Man)
Positive Representations with Zero Casimirs ,
Communications in Mathematical Physics, 405(91),
(2024)
|
arXiv Link
|
| 2022 |
Quantum cluster mutations and
reduced word graphs, Contemporary Mathematics (to appear)
|
arXiv Link
|
| 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 Phan Nhat Duy)
On the correspondence between perfect matchings and compatible pairs for affine cluster algebra |
arXiv:2312.08037
|
| 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) |
Link
|
| 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
|
--
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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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--
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Ph. D. Dissertation:
2012
|
Positive
Representation
and Harmonic Analysis of Split Real Quantum Groups
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