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Twisted fusion products and quantum twisted Q-systems
We obtain a complete characterization of the space of matrix elements dual to the graded multiplicity space arising from fusion products of Kirillov-Reshetikhin modules over special twisted current algebras defined by Kus and Ve ... Read More >
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Exchange matrices of I-boxes
Admissible chains of i-boxes are important combinatorial tools in the monoidal categorification of cluster algebras, as they provide seeds of the cluster algebra. In this paper, we explore the properties of maximal commuting fam ... Read More >
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Minimal Matchings for dP3 Cluster Variables
In previous work [LM17], Tri Lai and the second author studied a family of subgraphs of the dP3 brane tiling, called Aztec castles, whose dimer partition functions provide combinatorial formulas for cluster variables resulting f ... Read More >
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Cluster structures on spinor helicity and momentum twistor varieties
We study cluster structures on spinor helicity and momentum twistor varieties which describe the kinematic spaces of massless scattering (with or without dual conformal symmetry). Both are instances of partial flag varieties. We ... Read More >
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Multiplication formula for Hernandez and Leclerc's quivers with potentials
In this paper, we study multiplication formula of $F$-polynomial of representations of Hernandez and Leclerc's quivers with potentials. Since the truncated $q$-characters of some real simple modules over a quantum affine group $ ... Read More >
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Noncommutative frieze patterns with coefficients
Based on Berenstein and Retakh's notion of noncommutative polygons we introduce and study noncommutative frieze patterns. We generalize several notions and fundamental properties from the classic (commutative) frieze patterns to ... Read More >
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Representations of shifted quantum affine algebras and cluster algebras I. The s ...
We introduce a family of cluster algebras of infinite rank associated with root systems of type $A$, $D$, $E$. We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categorie ... Read More >
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Intersections of Dual $SL_3$-Webs
We introduce a topological intersection number for an ordered pair of $\operatorname{SL}_3$-webs on a decorated surface. Using this intersection pairing between reduced $(\operatorname{SL}_3,\mathcal{A})$-webs and a collection o ... Read More >
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Singularities and clusters
The aim of this note is to describe a geometric relation between simple plane curve singularities classified by simply laced Cartan matrices and cluster varieties of finite type also classified by the simply laced Cartan matrice ... Read More >
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A trilogy of mapping class group representations from three-dimensional quantum ...
For a punctured surface $\mathfrak{S}$, the author and Scarinci (arXiv:2112.13329) have recently constructed a quantization of a moduli space of Lorentzian metrics on the 3-manifold $\mathfrak{S} \times \mathbb{R}$ of constant s ... Read More >