Pieri resolutions for classical groups

We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij-S\"oderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given.Comment: 40 pages, no figures; v2: corrections to sections 2.2, 3.1, 3.3, and some typos; v3: important corrections to sections 2.2, 2.3 and Prop. 4.9 added, plus other minor corrections; v4: added assumptions to Theorem 3.6 and updated its proof; v5: Older versions misrepresented Peter Olver's results. See "New in this version" at the end of the introduction for more detail

Schubert varieties and finite free resolutions of length three

In this paper we describe the relationship between the finite free resolutions of perfect ideals in split format (for Dynkin formats) and certain intersections of opposite Schubert varieties with the big cell for homogeneous spaces $G/P$ where $P$ is a maximal parabolic subgroup.Comment: 12 pages; Dedicated to Laurent Gruson with thanks for his guidance and friendshi

State-Level Electricity Generation Efficiency: Do Restructuring and Regulatory Institutions Matter in the US?

This paper examines the impact of deregulation and the political support for it on the electric power industry using a consistent state-level electricity generation dataset for the US contiguous states from 1997-2014. Recent analyses of productivity growth suggests that institutional factors are important and we wish to study the role of deregulation as a statelevel institutional change through two measures: (a) restructuring and (b) the political support for it, measured by the majority political affiliation of public utility commissions. We find evidence of positive impacts of deregulation (both restructuring and the political support for it) on technical efficiency across the models estimated. Our preferred model which allows for the control for deregulation variables on the mean and variance of the inefficiency shows an average technical efficiency of 73.1 percent. The results of the marginal effects reveal that the impact of deregulation including its political support on inefficiency is negative and monotonic, with the potential reduction of 8.4 percent in the mean of technical inefficiency, thereby suggesting a compelling evidence for generation efficiency improvement via deregulation

Cost efficiency and electricity market structure: A case study of OECD countries

The OECD electricity sector has witnessed significant institutional restructuring over the past three decades. As a consequence, many power generation utilities now act as unregulated companies that technically compete to sell power on an open market. This paper analyses the performance in term of cost efficiency for electricity generation in OECD power sector while accounting for the impact of electricity market structures. We employ the short-run cost function in which capital stock is treated as a quasi-fixed factor input. Empirical models are developed for the cost function as a translog form and analysed using panel data of 25 countries during the period 1980 to 2009. We show that it is necessary to model latent country-specific heterogeneity in addition to time-varying inefficiency. The estimated economies of scale are adjusted to take account of the importance of the quasi-fixed capital input in determining cost behaviour, and long run constant returns to scale are verified for the OECD generation sector. The research findings suggest there is a significant impact of electricity market regulatory indicators on cost. In particular, public ownership and vertical integration are found to have significant and sizable increasing impacts on cost, thereby indicating policy lessons on the desirable ways to implement structural electricity generation reforms

Schubert complexes and degeneracy loci

Given a generic map between flagged vector bundles on a Cohen-Macaulay variety, we construct maximal Cohen-Macaulay modules with linear resolutions supported on the Schubert-type degeneracy loci. The linear resolution is provided by the Schubert complex, which is the main tool introduced and studied in this paper. These complexes extend the Schubert functors of Kra\'skiewicz and Pragacz, and were motivated by the fact that Schur complexes resolve maximal Cohen-Macaulay modules supported on determinantal varieties. The resulting formula in K-theory provides a "linear approximation" of the structure sheaf of the degeneracy locus, which can be used to recover a formula due to Fulton.Comment: 23 pages, uses tabmac.sty; v2: corrected typos and added reference

Poset structures in Boij-S\"oderberg theory

Boij-S\"oderberg theory is the study of two cones: the cone of cohomology tables of coherent sheaves over projective space and the cone of standard graded minimal free resolutions over a polynomial ring. Each cone has a simplicial fan structure induced by a partial order on its extremal rays. We provide a new interpretation of these partial orders in terms of the existence of nonzero homomorphisms, for both the general and the equivariant constructions. These results provide new insights into the families of sheaves and modules at the heart of Boij-S\"oderberg theory: supernatural sheaves and Cohen-Macaulay modules with pure resolutions. In addition, our results strongly suggest the naturality of these partial orders, and they provide tools for extending Boij-S\"oderberg theory to other graded rings and projective varieties.Comment: 23 pages; v2: Added Section 8, reordered previous section

Symmetric quivers, invariant theory, and saturation theorems for the classical groups

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product V_{N\lambda^1} \otimes ... \otimes V_{N\lambda^r} contains nonzero G-invariants for some N \ge 1, we show that the tensor product V_{2\lambda^1} \otimes ... \otimes V_{2\lambda^r} also contains nonzero G-invariants. This extends results of Kapovich-Millson and Belkale-Kumar and complements similar results for the general linear group due to Knutson-Tao and Derksen-Weyman. Our techniques involve the invariant theory of quivers equipped with an involution and the generic representation theory of certain quivers with relations.Comment: 29 pages, no figures; v2: updated Theorem 2.4 to odd characteristic, added Remark 3.9, added references, corrected some definitions and typo