Research Papers.

Hyperbolic geometry and generalizations. 

1. (with Tathagata Nayak) On Character variety of Anosov representations. arXiv: 2409.07316.

2. (with Rachna Aggarwal and Mukund Madhav Mishra) Conjugacy classes of automorphisms of the unit ball in a complex Hilbert space. arXiv: 2401.04951.

3. (with Sagar Kalane) Linking of quaternionic hyperbolic isometries. RG.2.2.33820.05763

4. (with Abhishek Mukherjee) On compositions of quaternionic Möbius transformations. RG.2.2.34147.98082.  to appear in: Contemporary Mathematics -- Proceedings of the 29th ICFIDCAA-2023, Amer. Math. Soc. Editors: Sudeb Mitra et. al. 

5. (with Sandipan Dutta and Tejbir Lohan) Classification and decomposition of quaternionic projective transformations. Linear Algebra Appl. 676 (2023), 66--87.

6. (with Sandipan Dutta and Tejbir Lohan) Limit sets of cyclic quaternionic Kleinian groups, Geom. Dedicata. 217, 61 (2023).

7. (with Rachna Aggarwal and Mukund Madhav Mishra) Fixed points and normal automorphisms of the unit ball of bounded operators on C^n,  Banach J. Math. Anal. 17(2), 31 (2023). 

8. (with Sagar B. Kalane) Local coordinates for complex and quaternionic hyperbolic pairs.  J. Aust. Math. Soc. 113 (2022), issue 1, 57--78. 

9. (with Abhishek Mukherjee and Devendra Tiwari) Discreteness of hyperbolic isometries by test maps. Osaka J. Math. 58 (2021), no. 3, 697--710.  

10. (with Mukund Madhav Mishra, Devendra Tiwari) On discreteness of subgroups of quaternionic hyperbolic isometries.  Bull. Aust. Math. Soc. 101 (2020), no. 2, 283--293. 

11. (with Sagar B. Kalane) On conjugation orbits of semisimple pairs in rank one. Forum Math.  31 (2019), no. 5, 1097–1118. 

12. (with Mukund Madhav Mishra, Devendra Tiwari) On generalized Jørgensen inequality in SL(2,C).  Siberian Electronic Mathematical Reports,  Vol 16 (2019), 542--546 .

13. (with Sagar B. Kalane) Quaternionic hyperbolic Fenchel-Nielsen coordinates.  Geom. Dedicata. 199 (2019), no. 1, 247--271. 

14. (with Abhishek Mukherjee and Sujit  K. Sardar) Test map and discreteness in SL(2, H), Glasgow Math.  J. 61(2019), 523--533. 

15. On generalized Jørgensen inequality in infinite dimension.  New York J. Math.  24 (2018), 865--869. 

16. (with Shiv Parsad)  Conjugation orbits of loxodromic pairs in SU(n,1).  Bull. Sci. Math. 148 (2018), 14--32. 

17. (with Shiv Parsad)  On Fenchel-Nielsen coordinates of surface group representations into SU(3,1). Math. Proc. Cambridge Philos. Soc. 165 (2018), no. 1, 1--23. 

18. (with Sean Lawton)  Invariants of pairs in SL(4, C) and SU(3,1). Proc. Amer. Math. Soc. 145 (2017), no.11, 4703--4715. 

19. (with Abhishek Mukherjee) Extremality of quaternionic Jorgensen inequality. Hiroshima Math. J. 47 (2017), 113--137. 

20. (with Cigole Thomas) Decomposition of complex hyperbolic isometries by involutions. Linear Algebra Appl. Volume 500 (2016), 63--76.

21. (with John R. Parker and Shiv Parsad) On the classification of unitary matrices. Osaka J. Math, vol 52, no. 4 (2015), 959--991.

22. (with Shiv Parsad)  Classification of quaternionic hyperbolic isometries. Conform. Geom. Dyn. 17 (2013), 68--76.

23.  Algebraic characterization of isometries of the complex and the quaternionic hyperbolic 3-spaces, Proc. Amer . Math. Soc, 141 (2013), 1017--1027.

24. The z-classes of quaternionic hyperbolic isometries. J. Group Theory, Volume 16, Issue 6 (2013), 941--964.

25. (with Wensheng Cao)  Algebraic characterization of  isometries of the complex and the quaternionic hyperbolic planes,  Geom. Dedicata, Volume 157, Number 1 (2012), 23--39.

26. (with Wensheng Cao)  Commuting isometries of the complex hyperbolic space, Proc. Amer. Math. Soc, 139 (2011), 3317--3326.

27. Algebraic characterization of the isometries of the hyperbolic 5-space,  Geom. Dedicata, Volume 144, Issue 1 (2010), 157--170.

28. (with Ravi S. Kulkarni) z-Classes of isometries of the hyperbolic space. Conform. Geom. Dyn. 13  (2009), 91--109.

Reversibility in Groups and Geometry.

1. (with Debattam Das) Combinatorial growth of reciprocal classes in the Hecke groups. arXiv:2411.00739

2.  (wih Debattam Das) On the z-classes in Fuchsian groups.  Indian J. Pure Appl. Math. (to appear)

3. (with Tejbir Lohan and Abhishek Mukherjee) Reversibility and algebraic characterization of the quaternionic Möbius transformations. arXiv 2401.15374.

4. (with Tejbir Lohan and Chandan Maity) Product of two involutions in complex special linear group. arXiv 2307.07967

5. (with Tejbir Lohan and Chandan Maity) Product of two involutions in quaternionic special linear group. Canada Math. Bull. (to appear)  arXiv:2410.01587

6. (with Tejbir Lohan and Chandan Maity) Real adjoint orbits of special linear groups, Illinois J Math. 68 (3)  (2024), 433-453.  arXiv: 2204.03624  

7. (with Chandan Maity)  A note on adjoint reality in simple complex Lie algebras. Math. Proc. R. Ir. Acad. 124A (2024), no. 1, 15--24.

8. (with Debattam Das)  Reciprocity in the Hecke groups.  New York J. Math. 30 (2024), 722--744. arXiv: 2307.00496

9. (with Chandan Maity) A note on reversibility of unipotent matrices,  arXiv: 2204.03623,   Essays on Geometry-- On the Occasion of Athanase Papadopoulos 65th Anniversary Conference,  Editors:  A. Muhammed Uludağ and Ayberk Zeytin, Springer Nature Switzerland AG, 2024.

10. (with Tejbir Lohan and Chandan Maity) Reversibility of affine transformations. Proc. Edinburgh. Math. Soc. 66,  Issue 4 (2023), 1217--1228.  doi:10.1017/S001309152300069X

11. (with Tejbir Lohan and Chandan Maity) Reversibility and real adjoint orbits of linear maps. In the book "Essays in Geometry, dedicated to NorbertA'Campo" (A. Papadopoulos, ed.), European Mathematical Society Press, Berlin, 2023. 

12. (with Chandan Maity) Reality of unipotent elements in classical Lie groups. Bull. Sci. Math. Volume 185 (2023), 103261. 

13. (with Tejbir Lohan) Reversibility of Hermitian isometries.  Linear Algebra Appl. 639 (2022), 159--176. 

14. (with Sushil Bhunia) Reversible quaternionic hyperbolic isometries. Linear Algebra Appl. Volume 591 (2020),  268--283.

15. (with Sudip Mazumder and Sujit K. Sardar)  Conjugate real classes in general linear groups.  J. Algebra Appl. Vol. 18, No. 3 (2019) 1950054. 

16. (with John R. Parker)  Reversible complex hyperbolic isometries. Linear Algebra Appl. Volume 438, Issue 6, (2013), 2728–2739. 

17. Conjugacy classes in Möbius groups, Geom. Dedicata, Volume 151, Number 1 (2011), 245--258.

Combinatorial groups.

1. (with Lokenath Kundu) The Dehn function for the palindromic automorphism group of free groups. arXiv: 2406.17409

2. (with Lokenath Kundu) On Dehn functions for family of polycyclic groups, arXiv:2403.16096.

3. (with Soumya Dey) Commutator subgroups of singular braid groups. J. Knot Theory Ramifications 31 (2022), no. 5,  Article no. 2250033. 

4. (with Tatyana Kozlovskaya, Oleg V. Mamonov) On some decompositions of the 3-strand singular braid group.  Topology Appl.  283, 107398, 2020. 

5. (with Swathi Krishna)  Palindromic width of graph of groups. Proc. Indian Acad. Sci. Math. Sci.  130, no. 1, Paper No. 22, 2020. 

6. (with Soumya Dey) Commutator subgroups of twin groups and Grothendieck's cartographical groups.  J. Algebra, Volume 530 (2019), 215-234. 

7. (with  Valeriy G. Bardakov, Mikhail V. Neshchadim) Commutator subgroup of virtual and welded braid groups. Int. J. Algebra Comput.  Vol. 29, No. 3 (2019), 507-533. 

8. (with Soumya Dey)  Commutator subgroups of welded braid groups. Topology Appl. 237 (2018), 7--20.

9. (with Valeriy G. Bardakov and Oleg V. Bryukhanov) On palindromic widths of some wreath products and nilpotent products. Proc. Indian Acad. Sci. Math. Sci., Volume 127, No. 1 (2017), 99--108.

10. (with  Valeriy G. Bardakov, Mikhail V. Neshchadim and Mahender Singh)  Palindromic automorphisms of free nilpotent groups.  J. Pure Appl. Algebra, Volume 221, Issue 2 (2017), 316--338.  

11. (with Valeriy G. Bardakov and Mahender Singh)  Palindromic automorphisms of free groups. J. Algebra, Volume 438 (2015), 260–282.

12. (with Valeriy G. Bardakov)  Palindromic width of finitely generated solvable groups. Comm Algebra, Volume 43, issue 11 (2015), 4809--4824.  

13. (with Valeriy G. Bardakov)  On palindromic width of certain extensions and quotients of free nilpotent groups.  Int. J. Algebra Comput. Vol. 24, No. 5 (2014), 553--567. 

14. (with Valeriy G. Bardakov)  Palindromic width of free nilpotent groups. J. Algebra 402 (2014), 379–391.

Geometric algebra. 

1. (with Shivam Arora)  z-Classes in finite groups of conjugate type (n,1). Proc. Indian Acad. Sci. Math. Sci. 128 (2018), no. 3, 128:31. 

2. (with Sudip Mazumder) Existence of an invariant form under a linear map. Indian J. Pure Appl. Math.  48 (2017), no.2, 211--220.

3. (with Ravi S. Kulkarni)  The z-classes of isometries.  J. Indian Math. Soc. Vol 81, no. 3-4 (2014), 245--258.

4. (with Ravi S. Kulkarni)  On the existence of invariant non-degenerate bilinear form under a linear map, Linear Algebra Appl. Volume 434, Issue 1 (2011), 89--103.

5. On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields,  Expo. Math. Volume 28, Issue 4  (2010), 351--356.

Books. 

• Geometry, Groups and Dynamics, Contemporary Mathematics, 2015, Volume: 639, American Mathematical Society. 

• Knot theory and its applications, Contemporary Mathematics, 2016, Volume: 670, American Mathematical Society.

Misc. 

• (with V. G. Bardakov, M. Singh, A. Vesnin and J. Wu) Some problems on knots, braids and automorphism groups, Siberian Electronic Mathematical Reports, Volume 12 (2015), 394--405. 

• Algebraic characterization of isometries of the hyperbolic 4-space, ISRN Geometry, vol. 2012, Article ID 757489,  doi:10.5402/2012/757489.