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Santanu Tantubay

Publications and source records attributed to Santanu Tantubay.

10 recordsLinked to original sources
arXiv2026

Representations of affine Nappi-Witten Lie algebras over polynomial algebras

In this paper, we study the representation theory of affine Nappi-Witten Lie algebra $\widehat{H_4}$ corresponding to the Nappi-Witten Lie algebra $H_4$. We completely classify all Cartan-free modules of rank one for the Nappi-Witten Lie algebra $H_4$. With the help of Cartan free $H_4$ modules we classify all Cartan-free modules of rank one over affine Nappi Witten Lie algebra. We also give a necessary and sufficient condition for these modules to be irreducible. Finally as an application we classify Cartan free modules of rank one for affine-Virasoro Nappi-Witten Lie algebras.

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arXiv2026

Whittaker Modules for W type Cartan Lie superalgebras

We consider the category of Whittaker modules for the Lie superalgebra $W_{m,n}$ of vector fields on $\mathbb{C}^{(m|n)}$. For any $\mathbf{a}\in \mathbb{C}^m$ we show the equivalence between the blocks $Ω_{\mathbf a}^{\widetilde{W}_{m,n}}$ of the category of $(AW)_{m,n}$-Whittaker modules with finite-dimensional Whittaker vector spaces and the category of finite-dimensional modules over certain Lie subsuperalgebra $T_{m,n}$ of $(AW)_{m,n}$ (and also of $\mathfrak{gl}{(m,n)})$. Then we apply the covering technique to study Whittaker $W_{m,n}$-modules and describe simple modules in the category $Ω_{\mathbf a}^{{W}_{m,n}}$ of such modules with finite-dimensional Whittaker vector spaces and with non-singular ${\mathbf a}$.

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arXiv2026

Whittaker constructions for quantum affine algebras

The goals of the paper are 3-fold. First, we revisit the construction of imaginary Whittaker modules over untwisted affine Kac-Moody Lie algebras. These modules are obtained using the parabolic induction from irreducible Whittaker modules over the associated Heisenberg Lie algebras. We show that the infinite support condition for Whittaker functions on Heisenberg Lie algebras is essential for irreducibility: when the support is finite the modules becomes reducible, yielding infinite chains of submodules. We establish the irreducibility criterion for the induced modules over affine Lie algebras and construct a large family of such modules. In particular, we obtain a class of irreducible modules on which the derivation acts neither semisimply nor freely. Second, we consider quantum analogs of imaginary Whittaker modules and establish irreducibility for a family of such modules. Finally, we prove the irreducibility of a certain class of modules over $\mathcal{U}_q(A_1^{(1)})$, which are not quantum deformations of irreducible modules for the affine Kac-Moody Lie algebra $A_1^{(1)}$. Our results can be potentially extended to all types of untwisted quantum affine algebras, providing a pathway toward their classification.

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arXiv2026

Automorphism groups and derivation algebras of Hamiltonian Lie algebras

In this paper, we compute the automorphism group and derivation algebra of the Hamiltonian Lie algebra $\mathcal{H}_{N}$ and its derived subalgebra $\mathcal{H}_{N}'$, where $N$ is an even positive integer. The automorphism groups are shown to be $\mathbf{GSp}_{N}(\mathbb{Z})\ltimes (\mathbb{\mathbb{K}}^{\times})^{N}$ for both Lie algebras and we prove that all derivations are inner for the Hamiltonian Lie algebra, also we compute the full derivation space for the derived subalgebra of Hamiltonian Lie algebra. Finally we compute the second cohomology group of Hamiltonian Lie algebra.

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arXiv2025

Representations of Hamiltonian Lie algebras

We consider the Shen-Larsson functor from the category of modules for the symplectic Lie algebra $\s$ to the category of modules for the Hamiltonian Lie algebra and show that it preserves the irreducibility except in the finite number of cases. The obtained irreducible modules for the Hamiltonian Lie algebra are cuspidal, whose weight multiplicities equal the dimension of the corresponding module of the symplectic Lie algebra. This extends well-known results for other Cartan type Lie algebras to the Hamiltonian case.

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arXiv2024

Simple Modules For Twisted Hamiltonian Extended Affine Lie Algebras

In this paper, we consider the twisted Hamiltonian extended affine Lie algebra (THEALA). We classify the irreducible integrable modules for these Lie algebras with finite-dimensional weight spaces when the finite-dimensional center acts non-trivially. This Lie algebra has a triangular decomposition, which is different from the natural triangular decomposition of twisted full toroidal Lie algebra. Any irreducible integrable module of it is the highest weight module with respect to the given triangular decomposition. In this paper, we describe the highest-weight space in detail.

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arXiv2023

Representations of Toroidal and Full toroidal Lie algebras over polynomial algebras

Toroidal Lie algebras are $n$ variable generalizations of affine Kac-Moody Lie algebras. Full toroidal Lie algebra is the semidirect product of derived Lie algebra of toroidal Lie algebra and Witt algebra, also it can be thought of $n$-variable generalization of Affine-Virasoro algebras. Let $\tilde{\mathfrak{h}}$ be a Cartan subalgebra of a toroidal Lie algebra as well as full toroidal Lie algebra without containing the zero-degree central elements. In this paper, we classify the module structure on $U(\tilde{\mathfrak{h}})$ for all toroidal Lie algebras as well as full toroidal Lie algebras which are free $U(\tilde{\mathfrak{h}})$-modules of rank 1. These modules exist only for type $A_l (l\geq 1)$, $C_l (l\geq2)$ toroidal Lie algebras and the same is true for full toroidal Lie algebras. Also, we determined the irreducibility condition for these classes of modules for both the Lie algebras.

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arXiv2022

Irreducible Integrable Modules for the full Toroidal Lie Algebras co-ordinated by Rational Quantum Torus

Let $\mathbb{C}_q$ be a non-commutative Laurent polynomial ring associated with a $(n+1)\times (n+1)$ rational quantum matrix $q$. Let $\mathfrak{sl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$ be the universal central extension of Lie subalgebra $\mathfrak{sl}_d(\mathbb{C}_q)$ of $\mathfrak{gl}_d(\mathbb{C}_q)$. Now let us take the Lie algebra $τ=\mathfrak{gl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$. Let $Der(\mathbb{C}_q)$ be the Lie algebra of all derivations of $\mathbb{C}_q$. Now we consider the Lie algebra $\tildeτ=τ\rtimes Der(\mathbb{C}_q)$, called as full toroidal Lie algebra co-ordinated by rational quantum tori. In this paper we get a classification of irreducible integrable modules with finite dimensional weight spaces for $\tildeτ$ with nonzero central action on the modules.

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