Zobrazeno 1 - 10
of 509
pro vyhledávání: '"Kang, Seok Jin"'
We categorify the quantum Borcherds-Bozec algebras by constructing their associated Khovanov-Lauda-Rouquier algebras.
Externí odkaz:
http://arxiv.org/abs/2406.18378
In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras $U_{q}(\mathfrak g)$ and their irreducible highest weight modules $V(\lambda)$. We show that the lower perfect graph (resp. upper perfect graph) of every lower pe
Externí odkaz:
http://arxiv.org/abs/2405.05666
Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B(\lambda)$ for the quantum affine algebras of types $A^{(2)}_{2n}$, $D^{(2)}_{n+1}$, $A^{(2)}_{2n-1}$, $D^{(1)}_n$, $B^{(1)}_n$ and $C^
Externí odkaz:
http://arxiv.org/abs/2403.11055
In this paper we construct Young wall models for the level $1$ highest weight and Fock space crystals of quantum affine algebras in types $E_6^{(2)}$ and $F_4^{(1)}$. Our starting point in each case is a combinatorial realization for a certain level
Externí odkaz:
http://arxiv.org/abs/2402.15829
We present and prove the Weyl-Kac type character formula for the irreducible highest weight modules over Borcherds-Bozec superalgebras with dominant integral highest weights.
Externí odkaz:
http://arxiv.org/abs/2401.15627
With the help of path realization and affine energy function, we give a Young wall construction of level-1 highest weight crystals $B(\lambda)$ over $U_{q}(G_{2}^{(1)})$ and $U_{q}(D_{4}^{(3)})$. Our construction is based on four different shapes of
Externí odkaz:
http://arxiv.org/abs/2211.07106
Let $U_{q}^{-}(\mathfrak g)$ be the negative half of a quantum Borcherds-Bozec algebra $U_{q}(\mathfrak g)$ and $V(\lambda)$ be the irreducible highest weight module with $\lambda \in P^{+}$. In this paper, we investigate the structures, properties a
Externí odkaz:
http://arxiv.org/abs/2211.02859
Publikováno v:
In Journal of Algebra 1 October 2024 655:376-404
We provide a construction of global bases for quantum Borcherds-Bozec algebras and their integrable highest weight representations.
Comment: All authors contribute equally
Comment: All authors contribute equally
Externí odkaz:
http://arxiv.org/abs/2108.04732
In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of ${B}(\infty)$
Externí odkaz:
http://arxiv.org/abs/2010.10985