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1. Universal Tensor Categories Generated by Dual Pairs

   https://doi.org/10.1007/s10485-021-09640-2  

   Chirvasitu, Alexandru; Penkov, Ivan (October 2021, Applied Categorical Structures)

   Abstract Let $$V_*\otimes V\rightarrow {\mathbb {C}}$$ V ∗ ⊗ V → C be a non-degenerate pairing of countable-dimensional complex vector spaces V and $$V_*$$ V ∗ . The Mackey Lie algebra $${\mathfrak {g}}=\mathfrak {gl}^M(V,V_*)$$ g = gl M ( V , V ∗ ) corresponding to this pairing consists of all endomorphisms $$\varphi $$ φ of V for which the space $$V_*$$ V ∗ is stable under the dual endomorphism $$\varphi ^*: V^*\rightarrow V^*$$ φ ∗ : V ∗ → V ∗ . We study the tensor Grothendieck category $${\mathbb {T}}$$ T generated by the $${\mathfrak {g}}$$ g -modules V , $$V_*$$ V ∗ and their algebraic duals $$V^*$$ V ∗ and $$V^*_*$$ V ∗ ∗ . The category $${{\mathbb {T}}}$$ T is an analogue of categories considered in prior literature, the main difference being that the trivial module $${\mathbb {C}}$$ C is no longer injective in $${\mathbb {T}}$$ T . We describe the injective hull I of $${\mathbb {C}}$$ C in $${\mathbb {T}}$$ T , and show that the category $${\mathbb {T}}$$ T is Koszul. In addition, we prove that I is endowed with a natural structure of commutative algebra. We then define another category $$_I{\mathbb {T}}$$ I T of objects in $${\mathbb {T}}$$ T which are free as I -modules. Our main result is that the category $${}_I{\mathbb {T}}$$ I T is also Koszul, and moreover that $${}_I{\mathbb {T}}$$ I T is universal among abelian $${\mathbb {C}}$$ C -linear tensor categories generated by two objects X , Y with fixed subobjects $$X'\hookrightarrow X$$ X ′ ↪ X , $$Y'\hookrightarrow Y$$ Y ′ ↪ Y and a pairing $$X\otimes Y\rightarrow {\mathbf{1 }}$$ X ⊗ Y → 1 where 1 is the monoidal unit. We conclude the paper by discussing the orthogonal and symplectic analogues of the categories $${\mathbb {T}}$$ T and $${}_I{\mathbb {T}}$$ I T . 

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2. Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

   https://doi.org/10.4153/S0008414X20000711  

   Gourevitch, Dmitry; Gustafsson, Henrik P.; Kleinschmidt, Axel; Persson, Daniel; Sahi, Siddhartha (February 2022, Canadian Journal of Mathematics)

   Abstract In this paper, we analyze Fourier coefficients of automorphic forms on a finite cover G of an adelic split simply-laced group. Let $$\pi $$ be a minimal or next-to-minimal automorphic representation of G . We prove that any $$\eta \in \pi $$ is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro–Shalika formula for cusp forms on $$\operatorname {GL}_n$$ . We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient, in terms of these Whittaker coefficients. A consequence of our results is the nonexistence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for G of type $$D_5$$ and $$E_8$$ with a view toward applications to scattering amplitudes in string theory. 

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3. Effective Leptophilic WIMPs at the e+e− collider

   https://doi.org/10.1007/JHEP04(2022)146  

   Barman, Basabendu; Bhattacharya, Subhaditya; Girmohanta, Sudhakantha; Jahedi, Sahabub (April 2022, Journal of High Energy Physics)

   A bstract We consider higher-dimensional effective (EFT) operators consisting of fermion dark matter (DM) connecting to Standard Model (SM) leptons upto dimension six. Considering all operators together and assuming the DM to undergo thermal freeze-out, we find out relic density allowed parameter space in terms of DM mass ( m χ ) and New Physics (NP) scale (Λ) with one loop direct search constraints from XENON1T experiment. Allowed parameter space of the model is probed at the proposed International Linear Collider (ILC) via monophoton signal for both Dirac and Majorana cases, limited by the centre-of-mass energy $$ \sqrt{s} $$ s =1 TeV, where DM mass can be probed within $$ {m}_{\chi }<\frac{\sqrt{s}}{2} $$ m χ < s 2 for the pair production to occur and Λ > $$ \sqrt{s} $$ s for the validity of EFT framework. 

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4. Search for direct production of electroweakinos in final states with missing transverse momentum and a Higgs boson decaying into photons in pp collisions at $$ \sqrt{s} $$ = 13 TeV with the ATLAS detector

   https://doi.org/10.1007/JHEP10(2020)005  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abed Abud, A.; Abeling, K.; Abhayasinghe, D. K.; Abidi, S. H.; AbouZeid, O. S.; Abraham, N. L.; Abramowicz, H.; et al (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract A search for a chargino-neutralino pair decaying via the 125 GeV Higgs boson into photons is presented. The study is based on the data collected between 2015 and 2018 with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 139 fb − 1 of pp collisions at a centre-of-mass energy of 13 TeV. No significant excess over the expected background is observed. Upper limits at 95% confidence level for a massless $$ {\tilde{\chi}}_1^0 $$ χ ˜ 1 0 are set on several electroweakino production cross-sections and the visible cross-section for beyond the Standard Model processes. In the context of simplified supersymmetric models, 95% confidence-level limits of up to 310 GeV in $$ m\left({\tilde{\chi}}_1^{\pm }/{\tilde{\chi}}_2^0\right) $$ m χ ˜ 1 ± / χ ˜ 2 0 , where $$ m\left({\tilde{\chi}}_1^0\right) $$ m χ ˜ 1 0 = 0 . 5 GeV, are set. Limits at 95% confidence level are also set on the $$ {\tilde{\chi}}_1^{\pm }{\tilde{\chi}}_2^0 $$ χ ˜ 1 ± χ ˜ 2 0 cross-section in the mass plane of $$ m\left({\tilde{\chi}}_1^{\pm }/{\tilde{\chi}}_2^0\right) $$ m χ ˜ 1 ± / χ ˜ 2 0 and $$ m\left({\tilde{\chi}}_1^0\right) $$ m χ ˜ 1 0 , and on scenarios with gravitino as the lightest supersymmetric particle. Upper limits at the 95% confidence-level are set on the higgsino production cross-section. Higgsino masses below 380 GeV are excluded for the case of the higgsino fully decaying into a Higgs boson and a gravitino. 

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5. Reconstruction Algorithms for Source Term Recovery from Dynamical Samples in Catalyst Models

   https://doi.org/10.1007/s00041-025-10184-5  

   Aldroubi, Akram; Gong, Le; Krishtal, Ilya; Miller, Brendan; Thareja, Sumati (August 2025, Journal of Fourier Analysis and Applications)

   Abstract This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form$$F=h+\eta $$ $F=h+\eta$, where$$\eta $$ $\eta$is a Lipschitz continuous background source. The primary objective is to estimate the unknown parameters of non-instantaneous sources$$h(t)=\sum \limits _{j=0}^M h_je^{-\rho _j(t-t_j)}\chi _{[t_j,\infty )}(t)$$ $h\left(t\right)=\sum _{j=0}^M{h}_j{e}^{-{\rho }_j(t-t_j)}{\chi }_{[t_j,\infty )}\left(t\right)$, such as the decay rates, initial intensities and activation times. We present two novel recovery algorithms that employ distinct sampling methods of the solution of the IVP. Algorithm 1 combines discrete and weighted average measurements, whereas Algorithm 2 uses a different variant of weighted average measurements. We analyze the performance of these algorithms, providing upper bounds on the recovery errors of the model parameters. Our focus is on the structure of the dynamical samples used by the algorithms and on the error guarantees they yield. 

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