数学・表現論・リー群とリー環，著書：フリーズの数学 スケッチ帖・多項式のラプソディー・代数群と軌道・幾何学と不変量・射影幾何学の考え方，フォロワーは相互フォローできる人のみ．原則鍵垢不可． Representation Theory, Lie Groups & Lie algebras, Frieze Patterns
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ALT Region between two overlapping circles (representations of horocycles in the Poincaré disk model of the hyperbolic plane). Length of each arc is given as 2 sinh(d/2), angle between tangents at the corners as 2 atan(sinh(d/2)), and area of the region as 4 sinh(d/2) - 4 atan(sinh(d/2))
![We construct an elliptic deformation Qₐ,b;q,ₚ(x) of positive rational numbers x by attaching Schlosser's small elliptic weights wₐ,b;q,ₚ(s,t) to prefixes of Stern–Brocot words. On positive integers n it gives Schlosser's elliptic numbers [n]ₐ,b;q,ₚ. Parameter shifts realize x ↦ x+1 and x ↦ x/(x+1), while a reciprocal parameter transformation gives an inversion formula. The Gaussian degeneration recovers the q-deformed rationals of Morier-Genoud and Ovsienko. The regular and negative elliptic continued fractions agree, since they evaluate the same word with the same ordered weights. The numerator and denominator satisfy weighted Farey recursions and, for rationals greater than 1, are the closure polynomials, or quiver F-polynomials, of the associated oriented type-A quivers. Finally, we express the vertex weights as normalized elliptic Euler expressions of balanced virtual torus representations.](https://pbs.twimg.com/media/HWwB-MuW0AABrcQ.png?name=orig)
ALT We construct an elliptic deformation Qₐ,b;q,ₚ(x) of positive rational numbers x by attaching Schlosser's small elliptic weights wₐ,b;q,ₚ(s,t) to prefixes of Stern–Brocot words. On positive integers n it gives Schlosser's elliptic numbers [n]ₐ,b;q,ₚ. Parameter shifts realize x ↦ x+1 and x ↦ x/(x+1), while a reciprocal parameter transformation gives an inversion formula. The Gaussian degeneration recovers the q-deformed rationals of Morier-Genoud and Ovsienko. The regular and negative elliptic continued fractions agree, since they evaluate the same word with the same ordered weights. The numerator and denominator satisfy weighted Farey recursions and, for rationals greater than 1, are the closure polynomials, or quiver F-polynomials, of the associated oriented type-A quivers. Finally, we express the vertex weights as normalized elliptic Euler expressions of balanced virtual torus representations.
