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Complex structures on two-step nilpotent Lie groups
Maria Laura Barberis
https://arxiv.org/abs/2508.05885 https://arxiv.org/pdf/2508.05885

Complex structures on two-step nilpotent Lie groups
We give a characterization of the $2$-step nilpotent Lie algebras whose corresponding Lie groups admit a left invariant complex structure. This is done by considering separately the cases when the complex structure is 2-step or 3-step nilpotent in the sense of [Cordero-Fernández-Gray-Ugarte, 2000]. We also study the Hermitian geometry 2-step nilpotent Lie groups. We show that if a left invariant Hermitian metric on such Lie group is pluriclosed, then the corresponding complex structure is 2-st…

Homogeneous locally nilpotent derivations on trinomial varieties
Kirill Rassolov
https://arxiv.org/abs/2509.08491 https://arxiv.org/pdf/2509.08491

Homogeneous locally nilpotent derivations on trinomial varieties
We consider the finest grading of the algebra of regular functions of a trinomial variety. An explicit description of locally nilpotent derivations that are homogeneous with respect to this grading is obtained.

Crosslisted article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Homogeneous locally nilpotent derivations on trinomial varieties
Kirill Rassolov

Modular analogs of character formulas and multiplicities of induced representations
Patrick Allen, Preston Wake, Robin Zhang
https://arxiv.org/abs/2508.06657 https://

Modular analogs of character formulas and multiplicities of induced representations
Let $G$ be a finite group, $k$ a characteristic-$p$ field, and $π$ be a simple $k[G]$-module. We show that if $π$ is in a $p$-nilpotent block with cyclic defect group, then $π$ appears with multiplicity at most one in the socle and cosocle of induced $k[G]$-modules that are multiplicity-free in characteristic zero and satisfy some additional hypotheses. We show that this applies, in particular, to certain Deligne--Lusztig modules $π$. As an application, we prove that well-known character fo…

Period maps at infinity
Mark Green, Phillip Griffiths, Colleen Robles
https://arxiv.org/abs/2509.08508 https://arxiv.org/pdf/2509.08508

Period maps at infinity
Let $\overline{B}$ be a smooth projective varieity, and $Z \subset \overline{B}$ a simple normal crossing divisor. Assume that $B = \overline{B} - Z$ admits a variation of pure, polarized Hodge structure. The divisor $Z$ is naturally stratified, and Schmid's nilpotent orbit theorem defines a family/variation of nilpotent orbits along each strata. We study the rich geometric structure encoded by this family, its relationship to the induced (quotient) variation of pure Hodge structure on the stra…

Learning Barycenters from Signature Matrices
Carlos Am\'endola, Leonard Schmitz
https://arxiv.org/abs/2509.07815 https://arxiv.org/pdf/2509.07815

Learning Barycenters from Signature Matrices
The expected signature of a family of paths need not be a signature of a path itself. Motivated by this, we consider the notion of a Lie group barycenter introduced by Buser and Karcher to propose a barycenter on path signatures. We show that every element of the free nilpotent Lie group is a barycenter of a group sample, where all but one sample element can be fixed arbitrarily. In the case of piecewise linear paths, we study the problem of recovering an underlying path corresponding to the ba…

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - I
Monika Yadav, Anuradha Sharma
https://arxiv.org/abs/2510.06082

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - I
Let $\mathscr{R}_{e,m}$ denote a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 3,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field $\mathscr{R}_{e,m}/\langle u \rangle$ of order $2^m.$ Suppose that $2 \in \langle u^κ\rangle \setminus \langle u^{κ+1}\rangle$ for some odd integer $κ$ with $3 \leq κ\leq e.$ In this paper, we first develop a recursive method to construct a self-orthogonal code $\mathscr{D}_e…

Batalin-Fradkin-Vilkovisky Quantization of FLPR model
Ansha S. Nair, Saurabh Gupta
https://arxiv.org/abs/2509.05632 https://arxiv.org/pdf/2509.05632…

Batalin-Fradkin-Vilkovisky Quantization of FLPR model
We quantize the Friedberg-Lee-Pang-Ren (FLPR) model within the framework of Batalin-Fradkin-Vilkovisky (BFV) formalism. We construct the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) charges using constraints and the fermionic gauge-fixing function by means of admissible gauge conditions. We also derive the BRST invariant effective action and corresponding symmetries of the model in both polar and Cartesian coordinates. Additionally, with the help of BRST charge, we demonstrate that the physical s…

Rost nilpotence for twisted Milnor hypersurfaces
Charles De Clercq, Evan Marth, Kirill Zainoulline
https://arxiv.org/abs/2510.07095 https://arxiv.org/pdf/2…

Rost nilpotence for twisted Milnor hypersurfaces
We show that the strong Rost nilpotence holds for motives of generic hyperplane sections of twisted Milnor hypersurfaces. Hence, we provide a new family of examples of smooth projective algebraic varieties which satisfy the strong Rost nilpotence principle. As an application, we compute the $p$-canonical dimension for such varieties.

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - II
Monika Yadav, Anuradha Sharma
https://arxiv.org/abs/2510.06069

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - II
Let $\mathcal{R}_{e,m}$ be a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 2,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field $\mathcal{R}_{e,m}/\langle u \rangle$ of order $2^m.$ Suppose that $2 \in \langle u^κ\rangle \setminus \langle u^{κ+1}\rangle$ for some even positive integer $ κ\leq e.$ In this paper, we provide a recursive method to construct a self-orthogonal code $\mathcal{C}_e$ of type $\{λ_…