Cluster structures on braid varieties
We show the existence of cluster $\mathcal {A} $-structures and cluster Poisson structures
on any braid variety, for any simple Lie group. The construction is achieved via weave …
on any braid variety, for any simple Lie group. The construction is achieved via weave …
Monoidal categorification of cluster algebras
SJ Kang, M Kashiwara, M Kim, S Oh - Journal of the American Mathematical …, 2018 - ams.org
We prove that the quantum cluster algebra structure of a unipotent quantum coordinate ring
$ A_q (\mathfrak {n}(w)) $, associated with a symmetric Kac–Moody algebra and its Weyl …
$ A_q (\mathfrak {n}(w)) $, associated with a symmetric Kac–Moody algebra and its Weyl …
Microlocal theory of Legendrian links and cluster algebras
R Casals, D Weng - arXiv preprint arXiv:2204.13244, 2022 - arxiv.org
We show the existence of quasi-cluster $\mathcal {A} $-structures and cluster Poisson
structures on moduli stacks of sheaves with singular support in the alternating strand …
structures on moduli stacks of sheaves with singular support in the alternating strand …
[图书][B] Quantum cluster algebra structures on quantum nilpotent algebras
K Goodearl, M Yakimov - 2017 - ams.org
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are
proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it …
proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it …
Tensor diagrams and cluster algebras
S Fomin, P Pylyavskyy - Advances in Mathematics, 2016 - Elsevier
The rings of SL (V) invariants of configurations of vectors and linear forms in a finite-
dimensional complex vector space V were explicitly described by Hermann Weyl in the …
dimensional complex vector space V were explicitly described by Hermann Weyl in the …
Monoidal categorification and quantum affine algebras
M Kashiwara, M Kim, S Oh, E Park - Compositio Mathematica, 2020 - cambridge.org
Monoidal categorification and quantum affine algebras Page 1 Monoidal categorification
and quantum affine algebras Masaki Kashiwara, Myungho Kim, Se-jin Oh and Euiyong Park …
and quantum affine algebras Masaki Kashiwara, Myungho Kim, Se-jin Oh and Euiyong Park …
Monoidal categorification and quantum affine algebras II
M Kashiwara, M Kim, S Oh, E Park - Inventiones mathematicae, 2024 - Springer
We introduce a new family of real simple modules over the quantum affine algebras, called
the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as …
the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as …
Cluster algebras and tilings for the m= 4 amplituhedron
The amplituhedron $ A_ {n, k, m}(Z) $ is the image of the positive Grassmannian $ Gr_ {k,
n}^{\geq 0} $ under the amplituhedron map $ Gr_ {k, n}^{\geq 0}\to Gr_ {k, k+ m} $ induced …
n}^{\geq 0} $ under the amplituhedron map $ Gr_ {k, n}^{\geq 0}\to Gr_ {k, k+ m} $ induced …
[PDF][PDF] Laurent phenomenon algebras
T Lam, P Pylyavskyy - arXiv preprint arXiv:1206.2611, 2012 - arxiv.org
arXiv:1206.2611v3 [math.RT] 21 Jan 2016 Page 1 arXiv:1206.2611v3 [math.RT] 21 Jan 2016
LAURENT PHENOMENON ALGEBRAS THOMAS LAM AND PAVLO PYLYAVSKYY Abstract …
LAURENT PHENOMENON ALGEBRAS THOMAS LAM AND PAVLO PYLYAVSKYY Abstract …
[PDF][PDF] Braid variety cluster structures, II: general type
P Galashin, T Lam, M Sherman-Bennett - arXiv preprint arXiv:2301.07268, 2023 - arxiv.org
arXiv:2301.07268v2 [math.AG] 7 Feb 2023 Page 1 BRAID VARIETY CLUSTER STRUCTURES,
II: GENERAL TYPE PAVEL GALASHIN, THOMAS LAM, AND MELISSA SHERMAN-BENNETT …
II: GENERAL TYPE PAVEL GALASHIN, THOMAS LAM, AND MELISSA SHERMAN-BENNETT …