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We formulate the Nahm transform in the context of parabolic Higgs bundles on P 1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are… (More)

This paper concerns the combinatorics of the orbit Hecke algebra associated with the orbit of a two sided Weyl group action on the Renner monoid of a finite monoid of Lie type, M. It is shown by Putcha in [12] that the Kazhdan-Lusztig involution ([6]) can be extended to the orbit Hecke algebra which enables one to define the R-polynomials of the intervals… (More)

- KÜRŞAT AKER
- 2009

This is an expository note describing the isomorphism classes of (algebraic) line bundles on pro-jective spaces in an elementary way. Our intention is to introduce the isomorphism classes of line bundles on a projective space in three different ways • By projective geometry, • By local coordinates, • As multiplicative group quotients. 0.1. Notations and… (More)

- KÜRŞAT AKER
- 2005

This paper is devoted to the study of a certain class of principal bundles on del Pezzo surfaces, which were introduced and studied by Friedman and Morgan in [10]: The two authors showed that there exists a unique principal bundle (up to isomorphism) on a given (Gorenstein) del Pezzo surface satisfying certain properties. We call these bundles almost… (More)

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