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- Shrawan Kumar
- 1994

Introduction. These are notes for my eight lectures given at the C.I.M.E. session on " Vector bundles on curves. New directions " held at Cetraro (Italy) in June 1995. The work presented here was done in collaboration with M.S. Narasimhan and A. Ra-manathan and appeared in [KNR]. These notes differ from [KNR] in that we have added three appendices (A)-(C)… (More)

- Prakash Belkale, Shrawan Kumar
- 2008

1 Introduction Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product ⊙ 0 on the cohomology of the homogenous spaces G/P and use this to give a more efficient solution of the eigenvalue problem and also for the problem of determining the existence of… (More)

- Shrawan Kumar, Niels Lauritzen, St, St, H I ( G / B, Su +9 others
- 1998

To the memory of A. Ramanathan Let G be a semisimple, simply connected algebraic group over an algebraically closed field of characteristic p > 0. Let U be the unipotent radical of a Borel subgroup B ⊂ G and u the Lie algebra of U. Springer [16] has shown for good primes, that there is a B-equivariant isomorphism U → u, where B acts through conjugation on U… (More)

- Prakash Belkale, Shrawan Kumar
- 2008

In this paper we consider the eigenvalue problem, intersection theory of homogenous spaces (in particular, the Horn problem) and the saturation problem for the symplectic and odd orthogonal groups. The classical embeddings of these groups in the special linear groups will play an important role. We deduce properties for these classical groups from the known… (More)

- Shrawan Kumar, John Millson
- 2008

The generalized triangle inequalities for rank 3 symmetric spaces of noncompact type. Abstract We compute the generalized triangle inequalities explicitly for all rank 3 symmetric spaces of noncompact type. For SL(4, C) there are 50 inequalities none of them redundant by [KTW]. For both Sp(6, C) and Spin(7, C) there are 135 inequalities of which 24 are… (More)

STUDY DESIGN
An axial rotation tester was designed and fabricated for the study. This allowed stabilization of seated subjects (hip down) and coupling of shoulders, permitting axial rotation and coupled lateral flexion. Using this device, a "flexion-extension free" axial rotation was executed for studying its characteristics.
OBJECTIVES
To determine the… (More)

Electromyographic (EMG) patterns of the trunk muscles were investigated during balance perturbations in a sitting position. Five healthy subjects (two females and three males, mean age 24.4 yr) were seated on a platform allowing rotational perturbations in the frontal and sagittal planes. Each of the forward, backward, right and left perturbations were… (More)

OBJECTIVES
To measure the cervical isometric force generation capacity of men and women reliably while seated in upright neutral posture.
DESIGN
The cervical muscle isometric strength was determined in flexion, extension, lateral flexion, anterolateral flexion and posterolateral extensions in an upright seated neutral posture. For this measurement a… (More)

The purpose of the current study was twofold: (1) to determine the isometric force and electromyographic (EMG) relationship of the sternocleidomastoid, splenii and trapezii muscles bilaterally in graded and maximal exertions in the sagittal, coronal and oblique planes. and (2) to develop regression equations to predict force based on the EMG scores. A newly… (More)

- Shrawan Kumar, M S Narasimhan
- 1997

Introduction Let G be a simple simply-connected connected complex affine algebraic group and let C be a smooth irreducible projective curve of genus ≥ 2 over the field of complex numbers C. Let M be the moduli space of semistable principal G-bundles on C and let Pic M be its Picard group, i.e., the group of isomorphism classes of algebraic line bundles on… (More)