Auslander–Reiten quiver of type D and generalized quantum affine Schur–Weyl duality

@article{Oh2016AuslanderReitenQO,
  title={Auslander–Reiten quiver of type D and generalized quantum affine Schur–Weyl duality},
  author={Se-jin Oh},
  journal={Journal of Algebra},
  year={2016},
  volume={460},
  pages={203-252}
}
  • Se-jin Oh
  • Published 15 August 2016
  • Mathematics
  • Journal of Algebra
View via Publisher
doi.org
12 Citations
Background Citations
4
Methods Citations
2

12 Citations

Auslander-Reiten quiver of type A and generalized quantum affine Schur-Weyl duality

The quiver Hecke algebra $R$ can be also understood as a generalization of the affine Hecke algebra of type $A$ in the context of the quantum affine Schur-Weyl duality by the results of Kang,…

Auslander–Reiten quiver and representation theories related to KLR-type Schur–Weyl duality

  • Se-jin Oh
  • Mathematics
    Mathematische Zeitschrift
  • 2018
We introduce new partial orders on the sequence positive roots and study the statistics of the poset by using Auslander–Reiten quivers for finite type ADE. Then we can prove that the statistics…

Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras

Twisted Coxeter elements and folded AR-quivers via Dynkin diagram automorphisms: I

We introduce and study the twisted adapted $r$-cluster point and its combinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded AR-quivers, of type $A_{2n+1}$ which are closely…

Combinatorial Auslander-Reiten quivers and reduced expressions

In this paper, we introduce the notion of combinatorial Auslander-Reiten(AR) quiver for commutation classes $[\widetilde{w}]$ of $w$ in finite Weyl group. This combinatorial object visualizes the…

Categorical Relations Between Langlands Dual Quantum Affine Algebras: Exceptional Cases

We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $${C_Q^{(t)} (t=1,2,3),…

Simplicity of tensor products of Kirillov--Reshetikhin modules: nonexceptional affine and G types

We show the denominator formulas for the normalized $R$-matrix involving two arbitrary Kirillov--Reshetikhin (KR) modules $W^{(k)}_{m,a}$ and $W^{(l)}_{p,b}$ in all nonexceptional affine types,…

Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras IV

Let $$U'_q(\mathfrak {g})$$Uq′(g) be a twisted affine quantum group of type $$A_{N}^{(2)}$$AN(2) or $$D_{N}^{(2)}$$DN(2) and let $$\mathfrak {g}_{0}$$g0 be the finite-dimensional simple Lie algebra…

Categorical relations between Langlands dual quantum affine algebras: doubly laced types

We prove that the Grothendieck rings of category CQ(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras IV

Let Uq′(g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

References

SHOWING 1-10 OF 30 REFERENCES

Auslander-Reiten quiver of type A and generalized quantum affine Schur-Weyl duality

The quiver Hecke algebra $R$ can be also understood as a generalization of the affine Hecke algebra of type $A$ in the context of the quantum affine Schur-Weyl duality by the results of Kang,…

Poincaré–Birkhoff–Witt bases and Khovanov–Lauda–Rouquier algebras

We generalize Lusztig’s geometric construction of the PBW bases of finite quantum groups of type ADE under the framework of [VaragnoloVasserot, J. reine angew. Math. 659 (2011)]. In particular, every…

Quantum Grothendieck rings and derived Hall algebras

We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain…

Homological properties of finite type Khovanov-Lauda-Rouquier algebras

We give an algebraic construction of standard modules (infinite dimensional modules categorifying the PBW basis of the underlying quantized enveloping algebra) for Khovanov-Lauda-Rouquier algebras in…

Quiver varieties and finite dimensional representations of quantum affine algebras

Introduction 145 1. Quantum affine algebra 150 2. Quiver variety 155 3. Stratification of M0 163 4. Fixed point subvariety 167 5. Hecke correspondence and induction of quiver varieties 169 6.…

Quantum affine algebras and affine Hecke algebras

One of the most beautiful results from the classical period of the representation theory of Lie groups is the correspondence, due to Frobenius and Schur, between the representations of symmetric…

Yangians, integrable quantum systems and Dorey's rule

It was pointed out by P. Dorey that the three-point couplings between the quantum particles in affine Toda field theories have a remarkable Lie-theoretic interpretation. It is also well known that…

Beyond Kirillov-Reshetikhin modules

In this survey, we shall be concerned with the category of finite-dimensional representations of the untwisted quantum affine algebras when the quantum parameter q is not a root of unity. We review…

Kirillov–Reshetikhin Conjecture: The General Case

We prove the Kirillov-Reshetikhin (KR) conjecture in the general case : for all twisted quantum affine algebras we prove that the characters of KR modules solve the twisted Q-system and we get…

A guide to quantum groups

Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. Quasitriangular…