Shifted quiver quantum toroidal algebra and subcrystal representations

@article{Noshita2022ShiftedQQ,
  title={Shifted quiver quantum toroidal algebra and subcrystal representations},
  author={Go Noshita and Akimi Watanabe},
  journal={Journal of High Energy Physics},
  year={2022}
}
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 particular, shifted QY acts on general subcrystals of the original BPS crystal. A trigonometric deformation called quiver quantum toroidal algebra (QQTA) was also proposed and shown to act on the same BPS crystal. Unlike QY, QQTA has a formal Hopf superalgebra structure which is useful in deriving… 

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References

SHOWING 1-10 OF 82 REFERENCES

q-deformation of corner vertex operator algebras by Miura transformation

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

Quantum W1+∞ subalgebras of BCD type and symmetric polynomials

The infinite affine Lie algebras of type ABCD, also called ĝl(∞), ô(∞), ŝp(∞), are equivalent to subalgebras of the quantum W1+∞ algebra. They have well-known representations on the Fock space of

Holomorphic field realization of SHc and quantum geometry of quiver gauge theories

A bstractIn the context of 4D/2D dualities, SHc algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of N=2$$ \mathcal{N}=2 $$

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

Quiver Yangian from crystal melting

Abstract We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric

Gauge theories from toric geometry and brane tilings

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of

Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds.

To a smooth local toric Calabi-Yau 3-fold $X$ we associate the Heisenberg double of the (equivariant spherical) Cohomological Hall algebra in the sense of Kontsevich and Soibelman. This Heisenberg

Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

A bstractReflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal gl1$$ \mathfrak{g}{\mathfrak{l}}_1 $$). Webs of DIM

Quantum algebraic approach to refined topological vertex

A bstractWe establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W1+∞ introduced by Miki. Our
...