• Corpus ID: 119579226

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

@article{Oh2016TwistedCE,
  title={Twisted Coxeter elements and folded AR-quivers via Dynkin diagram automorphisms: I},
  author={Se-jin Oh and Uhi Rinn Suh},
  journal={arXiv: Representation Theory},
  year={2016}
}
  • Se-jin OhU. Suh
  • Published 31 May 2016
  • Mathematics
  • arXiv: Representation Theory
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 related to twisted Coxeter elements and the non-trivial Dynkin diagram automorphism. As applications of the study, we prove that folded AR-quivers encode crucial information on the representation theory of quantum affine algebra $U_q'(B^{(1)}_{n+1})$ such as Dorey's rule and denominator formulas. 
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6 Citations
Background Citations
1
Methods Citations
2

6 Citations

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References

SHOWING 1-10 OF 32 REFERENCES

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…

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

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…

Quivers with relations for symmetrizable Cartan matrices I: Foundations

We introduce and study a class of Iwanaga–Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. These algebras generalize the path algebras of quivers…

Langlands Duality for Finite-Dimensional Representations of Quantum Affine Algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of Frenkel and Hernandez…

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…

PBW-bases of quantum groups.

here, s, r are non-negative integers, and r ̂ s; also, given a polynomial/in the variable v and an integer a, we denote by fa the polynomial obtained from / by replacing v by v°9 for V 2s _ #~ s…

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…

On Commutation Classes of Reduced Words in Weyl Groups

The case of the longest element w0 for the symmetric group S5 is considered and the fact that the set of commutation classes of reduced words of w0have nice symmetries and a topological structure is illustrated.