Topic
Minuscule representation
About: Minuscule representation is a research topic. Over the lifetime, 20 publications have been published within this topic receiving 250 citations.
Papers
TL;DR: In this article, the authors studied the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional $ \mathcal{N} = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold.
Abstract: We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional $ \mathcal{N} $
= 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping” of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E
6, E7 and E
8.
148 citations
TL;DR: In this article, the authors studied the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold.
Abstract: We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as `flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E_6, E_7 and E_8.
89 citations
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TL;DR: In this article, an algebraic model for the action of a regular element in a simple Lie algebra is given, and these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy classes of the Lie algebra.
Abstract: Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy classes of the Lie algebra. There are partial results in the case of a quasiminuscule representation, and a conjecture in the case of a general irreducible finite-dimensional representation. The method of proof is to relate the question to a problem concerning holomorphic principal bundles over cuspidal cubic curves.
14 citations
TL;DR: In this paper, the authors unify the two models in the case of the basic representation of an untwisted affine algebra, provided the underlying finite-dimensional algebra g possesses a minuscule representation (i.e., g is of classical or E 6, E 7 type).
12 citations
TL;DR: In this article, given a complex projective surface with an ADE singularity and p = 0, the authors constructed ADE bundles over it and its minimal resolution, and descibe their minuscule representation bundles in terms of configurations of (reducible) (-1)-curves.
Abstract: Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible) (-1)-curves.
12 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 2 |
| 2019 | 1 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 1 |
| 2014 | 3 |