q-deformation of corner vertex operator algebras by Miura transformation

@inproceedings{Harada2021qdeformationOC,
  title={q-deformation of corner vertex operator algebras by Miura transformation},
  author={Koichira Harada and Yutaka Matsuo and Go Noshita and Akimi Watanabe},
  year={2021}
}
Recently, Gaiotto and Rapcak proposed a generalization of WN algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as YL,M,N , is characterized by three non-negative integers L,M,N . It has a manifest triality automorphism which interchanges L,M,N , and can be obtained as a reduction of W1+∞ algebra with a “pit” in the plane partition representation. Later, Prochazka and Rapcak proposed a representation of YL,M,N in… 

A note on quiver quantum toroidal algebra

Abstract Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian $$ \mathfrak{gl} $$ gl 1. The characteristic feature

Shifted quiver quantum toroidal algebra and subcrystal representations

Abstract Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In

Quadratic relations of the deformed W-algebra for the twisted affine algebra A ( 2 ) 2

We revisit the free field construction of the deformed W -algebra by Frenkel and Reshetikhin, Commun. Math. Phys. 197, 1-31 (1998), where the basic W -current has been identified. Herein, we

Quadratic relations of the deformed W-superalgebra Wq,tA(M,N)

We find the free field construction of the basic W-current and screening currents for the deformed W-superalgebra Wq,tA(M,N) associated with Lie superalgebra of type A(M, N). Using this free field

5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$

We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition

References

SHOWING 1-10 OF 49 REFERENCES

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

A bstractWe analyze the asymptotic symmetry of higher spin gravity with M × M matrix valued fields, which is given by rectangular W-algebras with su(M) symmetry. The matrix valued extension is

On extensions of gl (m )n ⏜ Kac-Moody algebras and Calabi-Yau singularities

We discuss a class of vertex operator algebras Wm|n×∞ generated by a supermatrix of fields for each integral spin 1, 2, 3, . . . . The algebras admit a large family of truncations that are in

Quantum Groups and Quantum Cohomology

In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q,

Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal

Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators

Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in

The Maulik–Okounkov R-matrix from the Ding–Iohara–Miki algebra

The integrability of 4d $${\mathcal{N}}=2$$ gauge theories has been explored in various contexts, e.g., the Seiberg–Witten curve and its quantization. Recently, Maulik and Okounkov proposed that an

Webs of W-algebras

A bstractWe associate vertex operator algebras to (p, q)-webs of interfaces in the topologically twisted N=4$$ \mathcal{N}=4 $$ super Yang-Mills theory. Y-algebras associated to trivalent junctions

Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2

We construct a representation of the affine W-algebra of ${\mathfrak{g}}{\mathfrak{l}}_{r}$ on the equivariant homology space of the moduli space of Ur-instantons, and we identify the corresponding

The affine Yangian of gl1 revisited

Vertex algebras at the corner

A bstractWe introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N$$ \mathcal{N} $$ = 4 Super Yang Mills gauge theory. These vertex algebras satisfy