## 9 Citations

### Palindromic intervals in Bruhat order and hyperplane arrangements

- Mathematics
- 2019

An element $w$ of the Weyl group is called rationally smooth if the corresponding Schubert variety is rationally smooth. This happens exactly when the lower interval $[id,w]$ in the Bruhat order is…

### Rationally smooth Schubert varieties , inversion hyperplane arrangements , and Peterson translation

- 2014

We show that an element w of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement I(w) associated to the inversion set of w is inductively free, and the product (d1…

### Schubert varieties, inversion arrangements, and Peterson translation

- Mathematics
- 2014

We show that an element w of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement m(w) associated to the inversion set of w is inductively free, and the product (d 1…

### A pattern avoidance criterion for free inversion arrangements

- Mathematics
- 2014

We show that the hyperplane arrangement of a coconvex set in a finite root system is free if and only if it is free in corank 4. As a consequence, we show that the inversion arrangement of a Weyl…

### Sphericality and Smoothness of Schubert Varieties

- Mathematics
- 2018

We consider the action of the Levi subgroup of a parabolic subgroup that stabilizes a Schubert variety. We show that a smooth Schubert variety is a homogeneous space for a parabolic subgroup, or it…

### Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry

- Mathematics
- 2014

In 1990, Lakshmibai and Sandhya published a characterization of singular Schubert varieties in flag manifolds using the notion of pattern avoidance. This was the first time pattern avoidance was used…

### Solomon–Terao algebra of hyperplane arrangements

- MathematicsJournal of the Mathematical Society of Japan
- 2019

We introduce a new algebra associated with a hyperplane arrangement $\mathcal{A}$, called the Solomon-Terao algebra $\mbox{ST}(\mathcal{A},\eta)$, where $\eta$ is a homogeneous polynomial. It is…

### On a Class of Richardson Varieties

- Mathematics
- 2018

We investigate Schubert varieties that are spherical under a Levi subgroup action in a partial flag variety. We show that if the Schubert variety is nonsingular, then it is a spherical $L$-variety,…

## References

SHOWING 1-10 OF 38 REFERENCES

### Inversion arrangements and Bruhat intervals

- MathematicsJ. Comb. Theory, Ser. A
- 2011

### Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangements

- Mathematics
- 2010

We link Schubert varieties in the generalized flag manifolds with hyperplane arrangements. For an element of a Weyl group, we construct a certain graphical hyperplane arrangement. We show that the…

### Billey–Postnikov decompositions and the fibre bundle structure of Schubert varieties

- Mathematics
- 2014

A theorem of Ryan and Wolper states that a type A Schubert variety is smooth if and only if it is an iterated fibre bundle of Grassmannians. We extend this theorem to arbitrary finite type, showing…

### From Bruhat intervals to intersection lattices and a conjecture of Postnikov

- MathematicsJ. Comb. Theory, Ser. A
- 2009

### Bruhat order, smooth Schubert varieties, and hyperplane arrangements

- MathematicsJ. Comb. Theory, Ser. A
- 2008

### Betti numbers of smooth Schubert varieties and the remarkable formula of Kostant,Macdonald,Shapiro and Steinberg

- Mathematics
- 2010

The purpose of this note is to give a refinement of the product formula proved in [1] for the Poincare polynomial of a smooth Schubert variety in the flag variety of an algebraic group G over C. This…

### Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula

- Mathematics
- 1981

We define an n-arrangement as a finite family of hyperplanes through the origin in C "+1. In [11] and [12] we studied the free arrangement and defined its structure sequence (their definitions will…

### Lower bounds for Kazhdan-Lusztig polynomials from patterns

- Mathematics
- 2002

Kazhdan-Lusztig polynomials Px,w(q) play an important role in the study of Schubert varieties as well as the representation theory of semisimple Lie algebras. We give a lower bound for the values…

### Conjugacy classes in the Weyl group

- Mathematics
- 1970

Although both the conjugacy classes and irreducible characters of all the individual Weyl groups have been determined, no unified approach has been obtained which makes use of the common structure of…

### A pattern avoidance criterion for free inversion arrangements

- Mathematics
- 2014

We show that the hyperplane arrangement of a coconvex set in a finite root system is free if and only if it is free in corank 4. As a consequence, we show that the inversion arrangement of a Weyl…