I work in the field of Applied Functional Analysis. I am interested in groups of symmetries and work in areas which are connected to them: analysis, geometry, mathematical physics. Symmetries make the order and beauty not only in science but in the entire world surrounding us - flowers or architectural masterpieces contain patterns with symmetries of varous kinds.
. My research interests lie in studying the Hilbert spaces of analytic functions with reproducing kernels arising from group representations in complex and Clifford analysis and non-commutative geometry of homogeneous spaces based on the Erlangen programme.
Our work involves studying geometry of the elliptic, parabolic and hyperbolic homogeneous spaces based on the representation theory of the group SL(2, R), the special linear group of order 2 x 2 with real entries. The principal role here is played by Clifford algebras of matching types. The main aim for studying all these geometries is that we would like to develop the parabolic analytic function theory. Recently, we are working to find a suitable measure for the parabolic case.
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Mobius action by SL(2;R) on different homogeneous spaces Biswas D., Dutta S. By Proc. Nat. Acad. Sci. India Sect. A 92 23-29 (2022)
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GEOMETRIC INVARIANTS UNDER THE MÖBIUS ACTION OF THE GROUP SL(2; ) Biswas D., Dutta S. By Kragujevac Journal of Mathematics 45 925-941 (2021)
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Invariant projective properties under the action of the Lie group SL(3; R) on RP2 Biswas D., Dutta S. By (Communicated) - (2021)
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Geometry associated with the SL(3,R) action on Homogeneous space using the Erlangen program Biswas D., Rajwar I. By (communicated) - (2021)
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The geometry of invariants under the SL(3;R) action on projective space Biswas D., Rajwar I. By (under preparation) - (2022)
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The parabolic geometry generated by the Mobius action of SL(2;R) through Erlangen Program Biswas D., Gupta S. By (under preparation) - (2022)
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The Euler's and Pythogorean Identity for Dual numbers through the respective Adjoint and Mobius actions of SL(2; R) Gupta S., Biswas D. By (under preparation) - (2022)
- Co-Principal Investigator
Ph. D. Students
Himadri Lal Das
Area of Research: Applied Functional Analysis
Ipsita Rajwar
Area of Research: Applied Functional Analysis
Sneha Gupta
Area of Research: Applied Functional Analysis
