A functor for constructing R$R$‐matrices in the category O$\mathcal {O}$ of Borel quantum loop algebras
DOI10.1112/jlms.12815arXiv2301.10686OpenAlexW4386738085MaRDI QIDQ6199292
Publication date: 23 February 2024
Published in: Journal of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2301.10686
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Module categories in associative algebras (16D90) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23) Applications of Lie algebras and superalgebras to integrable systems (17B80) Special properties of functors (faithful, full, etc.) (18A22) Yang-Baxter equations (16T25) Cluster algebras (13F60) Braided monoidal categories and ribbon categories (18M15)
Cites Work
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- A cluster algebra approach to \(q\)-characters of Kirillov-Reshetikhin modules
- Cluster algebras and category \(\mathcal O\) for representations of Borel subalgebras of quantum affine algebras
- Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case
- Hidden Grassmann structure in the \(XXZ\) model. II: Creation operators
- Baxter's relations and spectra of quantum integrable models
- Quantum affine algebras
- Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
- Braid group action and quantum affine algebras
- Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
- Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras
- Higher-level eigenvalues of \(Q\)-operators and Schrödinger equation
- Minimal affinizations of representations of quantum groups: The rank 2 case
- An algebraic characterization of the affine canonical basis
- Yangians and Baxter's relations
- Categories over quantum affine algebras and monoidal categorification
- From the Drinfeld realization to the Drinfeld-Jimbo presentation of affine quantum algebras: injectivity
- Fundamental representations of quantum affine superalgebras and \(R\)-matrices
- Length-two representations of quantum affine superalgebras and Baxter operators
- On minimal affinizations of representations of quantum groups
- Discrete Miura opers and solutions of the Bethe ansatz equations
- Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case
- Folded quantum integrable models and deformed \(W\)-algebras
- RTT Realization of Quantum Affine Superalgebras and Tensor Products
- Beyond Kirillov-Reshetikhin modules
- Asymptotic representations and Drinfeld rational fractions
- Multiplicative Slices, Relativistic Toda and Shifted Quantum Affine Algebras
- The Kirillov-Reshetikhin conjecture and solutions of T-systems
- La R-matrice pour les algèbres quantiques de type affine non tordu1
- Monoidal categories of modules over quantum affine algebras of type A and B
- Quantum Grothendieck rings as quantum cluster algebras
- Stable maps, Q-operators and category 𝒪
- CRYSTAL BASES AND CATEGORIFICATIONS - CHERN MEDAL LECTURE
- Tensor Categories
- Quantum groups and quantum cohomology
- Geometric Realization of Dynkin Quiver Type Quantum Affine Schur–Weyl Duality
- Inverses of Cartan matrices of Lie algebras and Lie superalgebras
- Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras.
- Representations of Shifted Quantum Affine Algebras
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