Cohomology on Cotangent Bundles of Partial Flag Varieties in Type A
Abstract
Let G=SLn(C) and let P⊂ G be a standard parabolic subgroup with Levi factor L. For a G-dominant weight λ, consider the vector bundle on T*(G/P) obtained by pulling back the vector bundle on G/P associated to the irreducible L-module VL(λ)*. We express its cohomology as a direct limit of the cohomology of certain line bundles on a Bott--Samelson variety associated to an affine Kac-Moody group. This comparison yields vanishing of higher cohomology and shows that the global sections are generated over C[g*] by their degree-zero part VG(λ)*. Using these results together with the Braverman--Kazhdan intertwiners constructed in earlier joint work with A. Slipper, we give an explicit generating set for C[T*(SLn/[P,P])]. Finally, in an appendix joint with Tom Gannon, we combine these results to show the affinization Spec(C[T*(SLn/[P,P])]) has terminal singularities.
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BibTeX
@misc{grantcharov2026cohomology,
title = {{Cohomology on Cotangent Bundles of Partial Flag Varieties in Type A}},
author = {Nikolay Grantcharov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04670},
eprint = {2609.04670},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04670},
}
RIS
TY - UNPB
TI - Cohomology on Cotangent Bundles of Partial Flag Varieties in Type A
AU - Nikolay Grantcharov
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04670
UR - https://arxiv.org/abs/2609.04670
AB - Let G=SL_n(C) and let P⊂ G be a standard parabolic subgroup with Levi factor L. For a G-dominant weight λ, consider the vector bundle on T^*(G/P) obtained by pulling back the vector bundle on G/P associated to the irreducible L-module V_L(λ)^*. We express its cohomology as a direct limit of the cohomology of certain line bundles on a Bott--Samelson variety associated to an affine Kac-Moody group. This comparison yields vanishing of higher cohomology and shows that the global sections are generated over C[g^*] by their degree-zero part V_G(λ)^*. Using these results together with the Braverman--Kazhdan intertwiners constructed in earlier joint work with A. Slipper, we give an explicit generating set for C[T^*(SL_n/[P,P])]. Finally, in an appendix joint with Tom Gannon, we combine these results to show the affinization Spec(C[T^*(SL_n/[P,P])]) has terminal singularities.
ER -