The quantum toroidal algebra $$\widehat {\widehat {\mathfrak{g}{\mathfrak{l}_1}}}$$ : Calculation of characters of some representations as generating functions of plane partitions

Mutafyan, G. S.; Feigin, Boris

doi:10.1007/s10688-013-0006-z

Cited by 4 publications

(4 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The characters of quantum gl 1 toroidal algebra are computed as a sum over plane partitions [189,190]; and representation theory of quantum gl r toroidal algebra is discussed in [191,192]. 5.1.7.…”

Section: Dimension Uniform Descriptionmentioning

confidence: 99%

Quantum Geometry and Quiver Gauge Theories

Nekrasov

Pestun

Shatashvili

2018

Commun. Math. Phys.

150

273

View full text Add to dashboard Cite

We study macroscopically two dimensional N = (2, 2) supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product T d × R 2 ǫ of a d-dimensional torus and a two dimensional cigar with Ω-deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories, quantization of the moduli spaces of instantons on R 2−d × T 2+d and singular monopoles on R 2−d × T 1+d , for d = 0, 1, 2, and the Yangian Y ǫ (g Γ ), quantum affine algebra U aff q (g Γ ), or the quantum elliptic algebra U ell q,p (g Γ ) associated to Kac-Moody algebra g Γ for quiver Γ.

show abstract

Section: Dimension Uniform Descriptionmentioning

confidence: 99%

Quantum Geometry and Quiver Gauge Theories

Nekrasov

Pestun

Shatashvili

2018

Commun. Math. Phys.

150

273

View full text Add to dashboard Cite

show abstract

“…Such a plane partition can be viewed as an array formed by unit cubes, the i-th level of the array has the shape λ (i) . An explicit formula for the generating function of the plane partitions was conjectured in [9] and proved in [16]. For n m 1 it has the form…”

Section: Affine Supersymmetric Polynomialsmentioning

confidence: 98%

Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)

Molev,

Mukhin

2015

Preprint

View full text Add to dashboard Cite

We describe the algebra of invariants of the vacuum module associated with an affinization of the Lie superalgebra gl(1|1). We give a formula for its Hilbert-Poincaré series in a fermionic (cancellation-free) form which turns out to coincide with the generating function of the plane partitions over the (1, 1)-hook. Our arguments are based on a super version of the Beilinson-Drinfeld-Raïs-Tauvel theorem which we prove by producing an explicit basis of invariants of the symmetric algebra of polynomial currents associated with gl(1|1). We identify the invariants with affine supersymmetric polynomials via a version of the Chevalley theorem.

show abstract

Section: Affine Supersymmetric Polynomialsmentioning

confidence: 99%

“…λ . An explicit formula for the generating function of the plane partitions was conjectured in [9] and proved in [16]. For n m 1 ⩾ ⩾ it has the form ( ) ( ) ( )…”

Section: Affine Supersymmetric Polynomialsmentioning

confidence: 99%

Invariants of the vacuum module associated with the Lie superalgebra ${\mathfrak{gl}}(1| 1)$

Molev¹,

Mukhin²

2015

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We describe the algebra of invariants of the vacuum module associated with an affinization of the Lie superalgebra . We give a formula for its Hilbert–Poincaré series in a fermionic (cancellation-free) form which turns out to coincide with the generating function of the plane partitions over the -hook. Our arguments are based on a super version of the Beilinson–Drinfeld–Raïs–Tauvel theorem which we prove by producing an explicit basis of invariants of the symmetric algebra of polynomial currents associated with . We identify the invariants with affine supersymmetric polynomials via a version of the Chevalley theorem.

show abstract

The quantum toroidal algebra $$\widehat {\widehat {\mathfrak{g}{\mathfrak{l}_1}}}$$ : Calculation of characters of some representations as generating functions of plane partitions

Cited by 4 publications

References 3 publications

Quantum Geometry and Quiver Gauge Theories

Quantum Geometry and Quiver Gauge Theories

Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)

Invariants of the vacuum module associated with the Lie superalgebra ${\mathfrak{gl}}(1| 1)$

Contact Info

Product

Resources

About