The Grothendieck-Cousin complex of an induced representation

Kempf, George R.

doi:10.1016/0001-8708(78)90021-x

Cited by 71 publications

(74 citation statements)

References 14 publications

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“…Here δ αβ is the Grothendieck-Cousin (GC) operator andδ αβ is its complex conjugate (the a αβ are some non-zero real numbers). The GC operator acting from F α to F β corresponds to taking the singular part of a holomorphic differential form on X α along this divisor (see, for example, [26]). …”

Section: Summary Of the Resultsmentioning

confidence: 99%

“…Under our assumptions on the stratification X = α∈A X α the jth cohomology of the complex C • (E) coincides with H j (X, E) (see [26]). …”

Section: Cohomology Of the Superchargesmentioning

confidence: 99%

“…Then it corresponds to an integral weight µ of the group G. Let us suppose that µ is dominant, and so can be realized as the highest weight of an irreducible finite-dimensional representation V µ of G. We denote the corresponding line bundle by E µ . The GC complex of this line bundle is studied in detail in [26] (see also [14,46]), where it is shown that this complex coincides with the dual of the so-called Bernstein-Gelfand-Gelfand (BGG) resolution of V µ . The ith group of the GC complex C • (E µ ) is equal to…”

Section: Xαmentioning

confidence: 99%

See 2 more Smart Citations

Instantons beyond topological theory. I

Frenkel¹,

Losev²,

Nekrasov³

2011

J. Inst. Math. Jussieu

110

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Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyse the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.In Part I we describe the class of models under study and present our results in the case of onedimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyse explicitly. Part II will be devoted to supersymmetric two-dimensional sigma models and four-dimensional Yang-Mills theory. In Part III we will discuss non-supersymmetric models.

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Section: Summary Of the Resultsmentioning

confidence: 99%

“…Under our assumptions on the stratification X = α∈A X α the jth cohomology of the complex C • (E) coincides with H j (X, E) (see [26]). …”

Section: Cohomology Of the Superchargesmentioning

confidence: 99%

Section: Xαmentioning

confidence: 99%

See 1 more Smart Citation

Instantons beyond topological theory. I

Frenkel¹,

Losev²,

Nekrasov³

2011

J. Inst. Math. Jussieu

110

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show abstract

“…As in [22], we can calculate the character of F(X, 3£(w, Z)), and we get (without the assumption of anti-dominancy) Remark 3.9. In (3.8), we have assumed that X-p is anti-dominant.…”

Section: Lemma 35 // 1-p Is Anti-dominant Andmentioning

confidence: 97%

Further Generalization of Generalized Verma Modules

Gyoja¹

1993

Publ. Res. Inst. Math. Sci.

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“…Pour chaque caractère central χ considérons l'espace propre généralisé Ke78,pp. 373,374,384], les groupes H b Ω (L ) sont des g − B−modules ; c-à-d que l'action de l'algèbre de Lie de B (par retriction de celle de G) ≪ s'intègre ≫ en une action rationnelle de B.…”

Section: Suites De Compositionunclassified

Cohomologie des fibrés en droites sur les compactifications des groupes réductifs

Tchoudjem

2004

Annales Scientifiques de l’École Normale Supérieure

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The Grothendieck-Cousin complex of an induced representation

Cited by 71 publications

References 14 publications

Instantons beyond topological theory. I

Instantons beyond topological theory. I

Further Generalization of Generalized Verma Modules

Cohomologie des fibrés en droites sur les compactifications des groupes réductifs

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