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Gelfand-Kirillov dimension of the quantized algebra of regular functions on homogeneous spaces


Authors: Partha Sarathi Chakraborty and Bipul Saurabh
Journal: Proc. Amer. Math. Soc. 147 (2019), 3289-3302
MSC (2010): Primary 16P90, 17B37, 20G42
DOI: https://doi.org/10.1090/proc/14522
Published electronically: May 8, 2019
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Abstract: In this article, we prove that the Gelfand-Kirillov dimension of the quantized algebra of regular functions on certain homogeneous spaces of types $ A$, $ C$, and $ D$ is equal to the dimension of the homogeneous space as a real differentiable manifold.


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Partha Sarathi Chakraborty
Affiliation: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700010, India (On lien from Institute of Mathematical Sciences (HBNI), CIT Campus, Taramani, Chennai, 600113, India)
Email: parthacsarathi.isi.smu@gmail.com, parthacsarathi@yahoo.co.in

Bipul Saurabh
Affiliation: Indian Institute of Technology, Gandhinagar, Palaj, Gandhinagar, 382355, India
Email: saurabhbipul2@gmail.com, bipul.saurabh@iitgn.ac.in

DOI: https://doi.org/10.1090/proc/14522
Keywords: Quantized function algebra, Weyl group, Gelfand-Kirillov dimension
Received by editor(s): January 11, 2018
Received by editor(s) in revised form: October 12, 2018, and November 6, 2018
Published electronically: May 8, 2019
Additional Notes: The first author acknowledges support from Swarnajayanthi Fellowship Award Project No. DST/SJF/MSA-01/2012-13.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2019 American Mathematical Society