Diagram automorphisms of quiver varieties

Henderson, Anthony; Licata, Anthony

doi:10.1016/j.aim.2014.08.007

Cited by 20 publications

(43 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5 More recently, in [19] and [21], nilpotent orbits and Slodowy slices have been used in the study of 6d N " p2, 0q theories on Riemann surfaces. Relationships between diagram automorphisms of quiver varieties and Slodowy slices are explored in [22]. In [23] the algebras of polynomial functions on Slodowy slices were shown to be related to classical (finite and affine) W-algebras.…”

mentioning

confidence: 99%

“…The sub-regular Slodowy slices of non-simply laced algebras match those of specific simply laced algebras, in accordance with their Kleinian singularities, as listed in table 1. In the case of Slodowy slices of C n nilpotent orbits with vector partitions of type p2n´k, kq, it was identified in [22] that these isomorphisms with D n`1 extend further down the Hasse diagram: S N ,Cp2n´k,kq " S N ,Dp2n´k`1,k`1q . This occurs due to matching chains of Kraft-Procesi transitions [13] within such slices.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quiver theories and formulae for Slodowy slices of classical algebras

2019

View full text Add to dashboard Cite

We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra g. We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone S XN of g. We calculate refined Hilbert series for Classical algebras up to rank 4 (and A 5 ), and find descriptions of their representation matrix generators as algebraic varieties encoding the relations of the chiral ring. We also analyse a class of dual quiver theories, whose Coulomb branches are intersections S X N ; such dual quiver theories exist for the Slodowy slices of A algebras, but are limited to a subset of the Slodowy slices of BCD algebras. The analysis opens new questions about the extent of 3d mirror symmetry within the class of SCFTs known as T ρ σ pGq theories. We also give simple group theoretic formulae for the Hilbert series of Slodowy slices; these draw directly on the SU p2q embedding into G of the associated nilpotent orbit, and the Hilbert series of the nilpotent cone.

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Quiver theories and formulae for Slodowy slices of classical algebras

2019

View full text Add to dashboard Cite

show abstract

“…A more general isomorphism σ f 0 can be defined by using a f 0 , a generalization of a, in Section 3.3. To control its order in this case, f 0 has to satisfy a compatibility assumption in [HL14]. Specifically, we can identify W i with W a(i) for all i ∈ I due to w i = w a(i) .…”

Section: Geometric Properties Of σ-Quiver Varietiesmentioning

confidence: 99%

“…As a consequence, we deduce the rectangular symmetry for classical groups. The symmetry provides a natural home for the recent results of [HL14,W15] on the interactions of two-row Slodowy slices of symplectic and orthogonal groups. We also briefly discuss a geometric version of Kraft-Procesi's column-removal and row-removal reductions for classical groups in [KP82,Proposition 13.5].…”

Section: Example Ii: Partial Resolutions Of Nilpotent Slodowy Slicesmentioning

confidence: 99%

“…In a similar manner for n being odd, one gets similar diagrams with the pair (sp w , o w ) replaced by either (sp w , sp w ) or (o w , o w ). Now we single out a special pair of (v, w) for (121) and (122) in the following example and relate it to the works of Henderson-Licata [HL14] and Wilbert [W15] (see also [ES12]).…”

Section: Example Ii: Partial Resolutions Of Nilpotent Slodowy Slicesmentioning

confidence: 99%

See 1 more Smart Citation

Quiver varieties and symmetric pairs

2019

Represent. Theory

View full text Add to dashboard Cite

We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram isomorphism, a reflection functor and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties. In type A case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.

show abstract

The small E8 instanton and the Kraft Procesi transition

Hanany

Mekareeya

2018

J. High Energ. Phys.

135

View full text Add to dashboard Cite

One of the simplest (1, 0) supersymmetric theories in six dimensions lives on the world volume of one M5 brane at a D type singularity C 2 /D k . The low energy theory is given by an SQCD theory with Sp(k − 4) gauge group, a precise number of 2k flavors which is anomaly free, and a scale which is set by the inverse gauge coupling. The Higgs branch at finite coupling H f is a closure of a nilpotent orbit of D 2k and develops many more flat directions as the inverse gauge coupling is set to zero (violating a standard lore that wrongly claims the Higgs branch remains classical). The quaternionic dimension grows by 29 for any k and the Higgs branch stops being a closure of a nilpotent orbit for k > 4, with an exception of k = 4 where it becomes min E 8 , the closure of the minimal nilpotent orbit of E 8 , thus having a rare phenomenon of flavor symmetry enhancement in six dimensions. Geometrically, the natural inclusion of H f ⊂ H ∞ fits into the Brieskorn Slodowy theory of transverse slices, and the transverse slice is computed to be min E 8 for any k > 3. This is identified with the well known small E 8 instanton transition where 1 tensor multiplet is traded with 29 hypermultiplets, thus giving a physical interpretation to the geometric theory. By the analogy with the classical case, we call this the Kraft Procesi transition. arXiv:1801.01129v3 [hep-th] 6 Jul 20181 There exist other examples of Higgs branch flows in 6d in which n T , n H , and n V all change. An example of this is a theory of N M5-branes on C 2 /D k discussed in section 3 of this paper. The number of tensor multiplets at a generic point of the tensor branch is n T = 2N −1, whereas there are N − 1 tensor multiplets left at the end of the Higgs branch flow [5]. In this theory, 29n T + n H − n V is equal to 30(N − 1) + dim(SO(2k)) + 1, which is proportional to the anomaly coefficient δ given by (3.3).

show abstract

Diagram automorphisms of quiver varieties

Cited by 20 publications

References 26 publications

Quiver theories and formulae for Slodowy slices of classical algebras

Quiver theories and formulae for Slodowy slices of classical algebras

Quiver varieties and symmetric pairs

The small E8 instanton and the Kraft Procesi transition

Contact Info

Product

Resources

About