Related papers: Kirillov-Reshetikhin crystals $B^{7,s}$ for type $…
We show that the wall crossing bijections between simples of the category O of the rational Cherednik algebras reduce to particular crystal isomorphisms which can be computed by a simple combinatorial procedure on multipartitions of fixed…
Single crystals of La(O,F)BiSSe were successfully grown by a CsCl flux method. Single crystal X-ray structural analysis revealed that the crystal structure is isostructural with BiS$_2$- or BiSe$_2$-based compounds with space group $P4/nmm$…
Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Recently $\beta$-Mn structure-type Co-Zn-Mn…
To each oriented closed combinatorial manifold we assign the set (with repetitions) of isomorphism classes of links of its vertices. The obtained transformation L is the main object of study of the present paper. We pose a problem on the…
The rigged configuration realization $RC(\infty)$ of the crystal $B(\infty)$ was originally presented as a certain connected component within a larger crystal. In this work, we make the realization more concrete by identifying the elements…
The crystal structure of potassium doped picene with an exact stoichiometry (K3C22H14, K3picene from here onwards) has been theoretically determined within Density Functional Theory allowing complete variational freedom of the crystal…
A Littelmann path model is constructed for crystals pertaining to a not necessarily symmetrizable Borcherds-Cartan matrix. Here one must overcome several combinatorial problems coming from the imaginary simple roots. The main results are an…
We have successfully synthesized single crystals, solved the crystal structure, and studied the magnetic properties of a new family of copper halides (C$_4$H$_{14}$N$_2$)Cu$_2X_6$ ($X$= Cl, Br). These compounds crystallize in an…
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
X-ray diffraction with photon energies near the Ru L$_2$-absorption edge was used to detect resonant reflections characteristic of a G-type superstructure in RuSr$_2$GdCu$_2$O$_8$ single crystals. A polarization analysis confirms that these…
We define geometric/unipotent crystal structure on unipotent subgroups of semi-simple algebraic groups. We shall show that in $A_n$-case, their ultra-discretizations coincide with crystals obtained by generalizing Young tableaux.
Let $\mathfrak{g}$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$. It is conjectured that for each Dynkin node $k \in I \setminus \{0\}$ the affine Lie algebra $\mathfrak{g}$ has a positive geometric crystal. In this…
A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich - physics/0401107) is applied to a perfect $\alpha$-quartz crystal…
We initiate a new approach to the study of the combinatorics of several parametrizations of canonical bases. In this work we deal with Lie algebras of type $A$. Using geometric objects called Rhombic tilings we derive a "crossing formula"…
Let G be a connected split reductive group over a complete discrete valuation ring of mixed characteristic. We use the theory of intermediate extensions due to Abe-Caro and arithmetic Beilinson-Bernstein localization to classify irreducible…
In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For…
An infinite crystal can be constructed by an infinite number of parallel two-dimensional (hkl) crystal planes coupled to each other. For crystals with negligible spin-orbit coupling, we report a rigorous proof of a criterion on the…
This is a continuation of [15, 16]. We shall show that for type D_n the realization of crystal bases obtained from the decorated geometric crystals in [2] coincides with the polyhedral realizations of crystal bases.
Gasharov introduced the combinatorial objects known as $P$-arrays to prove $s$-positivity for the chromatic symmetric functions of incomparability graphs of (3+1)-free posets. We define a crystal, a directed colored graph with some…
We show that a connected regular $A_2$-crystal (the crystal graph of an irreducible representation of $sl_3$) can be produced from two half-grids by replicating them and glying together in a certain way. Also some extensions and related…